{"id":3437,"date":"2022-03-24T17:48:32","date_gmt":"2022-03-24T17:48:32","guid":{"rendered":"https:\/\/stage-wp.10minuteschool.com\/?p=3437"},"modified":"2022-03-24T13:43:51","modified_gmt":"2022-03-24T13:43:51","slug":"time-dilation-length-contraction","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/time-dilation-length-contraction\/","title":{"rendered":"\u0995\u09be\u09b2 \u09a6\u09c0\u09b0\u09cd\u0998\u09be\u09af\u09bc\u09a8, \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09b8\u0982\u0995\u09cb\u099a\u09a8 \u0993 \u09ad\u09b0 \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf (Time dilation, length contraction and increase of mass)"},"content":{"rendered":"<h2><b>\u0986\u09aa\u09c7\u0995\u09cd\u09b7\u09bf\u0995\u09a4\u09be \u09a4\u09a4\u09cd\u09a4\u09cd\u09ac \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09b8\u09ae\u09af\u09bc \u09aa\u09cd\u09b0\u09b8\u09be\u09b0\u09a3 (<\/b><b>Time dilation according to the theory of relativity<\/b><b>)<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">\u0995\u09cb\u09a8\u09cb \u099c\u09a1\u09bc \u09ac\u09be \u09b8\u09cd\u09a5\u09bf\u09b0 \u0995\u09be\u09a0\u09be\u09ae\u09cb\u09a4\u09c7 \u09b8\u0982\u0998\u099f\u09bf\u09a4 \u0998\u099f\u09a8\u09be \u0989\u0995\u09cd\u09a4 \u0995\u09be\u09a0\u09be\u09ae\u09cb \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u0985\u09a8\u09cd\u09af \u0995\u09cb\u09a8\u09cb \u0995\u09be\u09a0\u09be\u09ae\u09cb \u09a5\u09c7\u0995\u09c7 \u09b2\u0995\u09cd\u09b7\u09cd\u09af \u0995\u09b0\u09b2\u09c7 \u09a6\u09c7\u0996\u09be \u09af\u09be\u09ac\u09c7 \u0998\u099f\u09a8\u09be\u09b0 \u09b8\u09ae\u09af\u09bc \u09ac\u09cd\u09af\u09ac\u09a7\u09be\u09a8 \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf \u09aa\u09c7\u09af\u09bc\u09c7\u099b\u09c7\u0964 \u098f \u09ac\u09bf\u09b7\u09af\u09bc\u099f\u09bf\u0995\u09c7 \u09b8\u09ae\u09af\u09bc \u09aa\u09cd\u09b0\u09b8\u09be\u09b0\u09a3 \u09ac\u09be \u0995\u09be\u09b2 \u09a6\u09c0\u09b0\u09cd\u0998\u09be\u09af\u09bc\u09a8 (<\/span>Time dilation) <span style=\"font-weight: 400;\">\u09ac\u09b2\u09c7\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09ac\u09c1\u099d\u09be\u09b0 \u09b8\u09c1\u09ac\u09bf\u09a7\u09be\u09b0\u09cd\u09a5\u09c7 \u09a7\u09b0\u09be \u09af\u09be\u0995 \u09ae\u09b9\u09be\u09b6\u09c2\u09a8\u09cd\u09af\u09c7 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8\u0995\u09be\u09b0\u09c0 \u0995\u09cb\u09a8\u09cb \u09ac\u09cd\u09af\u0995\u09cd\u09a4\u09bf \u09ae\u09b9\u09be\u09b6\u09c2\u09a8\u09cd\u09af\u09af\u09be\u09a8\u09c7 \u098f\u0995\u099f\u09bf \u0998\u099f\u09a8\u09be <span class=\"katex-eq\" data-katex-display=\"false\">t_0<\/span><\/span><span style=\"font-weight: 400;\"> \u09b8\u09ae\u09df \u09a7\u09b0\u09c7 \u09aa\u09b0\u09cd\u09af\u09ac\u09c7\u0995\u09cd\u09b7\u09a3 \u0995\u09b0\u09b2\u09c7\u09a8\u0964 \u09ad\u09c2\u09aa\u09c3\u09b7\u09cd\u09a0 \u09a5\u09c7\u0995\u09c7 \u0995\u09cb\u09a8\u09cb \u09ac\u09cd\u09af\u0995\u09cd\u09a4\u09bf \u0993\u0987 \u098f\u0995\u0987 \u0998\u099f\u09a8\u09be t \u09b8\u09ae\u09af\u09bc \u09a7\u09b0\u09c7 \u09aa\u09b0\u09cd\u09af\u09ac\u09c7\u0995\u09cd\u09b7\u09a3 \u0995\u09b0\u09b2\u09c7\u09a8\u0964 \u09a4\u09be\u09b9\u09b2\u09c7 \u09a6\u09c7\u0996\u09be \u09af\u09be\u09ac\u09c7 \u09af\u09c7, \u09b8\u09ae\u09df <span class=\"katex-eq\" data-katex-display=\"false\">t<\/span>, \u09b8\u09ae\u09df <span class=\"katex-eq\" data-katex-display=\"false\">t_0<\/span><\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">\u0985\u09aa\u09c7\u0995\u09cd\u09b7\u09be \u09a6\u09c0\u09b0\u09cd\u0998\u09a4\u09ae \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n<p><b>\u09ac\u09cd\u09af\u09be\u0996\u09cd\u09af\u09be\u0983<\/b><span style=\"font-weight: 400;\"> \u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, S \u098f\u09ac\u0982 S\u2019 \u09a6\u09c1\u099f\u09bf \u0995\u09be\u09a0\u09be\u09ae\u09cb\u0964 \u098f\u09a6\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 S \u09b8\u09cd\u09a5\u09bf\u09b0 \u0995\u09be\u09a0\u09be\u09ae\u09cb\u0964 \u098f\u0995\u09c7 \u0985\u099a-\u0995\u09be\u09a0\u09be\u09ae\u09cb \u09ac\u09b2\u09bf\u0964 \u0985\u09aa\u09b0\u099f\u09bf S\u2019 \u0995\u09be\u09a0\u09be\u09ae\u09cb \u09af\u09be <\/span><span style=\"font-weight: 400;\"> \u09ac\u09c7\u0997\u09c7 +ve X \u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 S \u0995\u09be\u09a0\u09be\u09ae\u09cb \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2\u0964 \u098f\u0995\u09c7 \u099a-\u0995\u09be\u09a0\u09be\u09ae\u09cb \u09ac\u09b2\u09bf\u0964<\/span><\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-9230 size-full\" src=\"https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/13.1-4.png\" alt=\"time dilation\" width=\"1052\" height=\"667\" srcset=\"https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/13.1-4.png 1052w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/13.1-4-300x190.png 300w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/13.1-4-1024x649.png 1024w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/13.1-4-768x487.png 768w\" sizes=\"(max-width: 1052px) 100vw, 1052px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-weight: 400;\">\u09a7\u09b0\u09bf \u099a-\u0995\u09be\u09a0\u09be\u09ae\u09cb\u09b0 x\u2019 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u098f\u0995\u099f\u09bf \u0998\u09a1\u09bc\u09bf \u09b0\u09af\u09bc\u09c7\u099b\u09c7\u0964 \u0989\u0995\u09cd\u09a4 \u0995\u09be\u09a0\u09be\u09ae\u09cb\u09a4\u09c7 \u09b8\u09cd\u09a5\u09bf\u09a4\u09bf\u09b6\u09c0\u09b2 \u098f\u0995\u099c\u09a8 \u09aa\u09b0\u09cd\u09af\u09ac\u09c7\u0995\u09cd\u09b7\u0995 \u0995\u09cb\u09a8\u09cb \u0998\u099f\u09a8\u09be\u09b0 \u09b8\u09ae\u09af\u09bc <span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{t}_{1}'<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0\u09b2\u09c7\u09a8\u0964 \u0985\u099a-\u0995\u09be\u09a0\u09be\u09ae\u09cb\u09b0 \u098f\u0995\u099c\u09a8 \u09aa\u09b0\u09cd\u09af\u09ac\u09c7\u0995\u09cd\u09b7\u0995 <\/span><span style=\"font-weight: 400;\"> \u09ac\u09c7\u0997\u09c7 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u09b9\u0993\u09af\u09bc\u09be\u09af\u09bc \u0993\u0987 \u0998\u099f\u09a8\u09be\u09b0 \u09b8\u09ae\u09af\u09bc <span class=\"katex-eq\" data-katex-display=\"false\">t_1<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0\u09b2\u09c7\u09a8\u0964 \u098f\u0996\u09a8 <a href=\"https:\/\/stage-wp.10minuteschool.com\/lorentzs-transformation\/\">\u09b2\u09b0\u09c7\u099e\u09cd\u099c-\u098f\u09b0 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u09b0\u09c2\u09aa\u09be\u09a8\u09cd\u09a4\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3<\/a> \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 (<\/span><span style=\"font-weight: 400;\">Lorentz&#8217;s inverse transformation<\/span><span style=\"font-weight: 400;\">)<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{t}_{1}=\\frac{\\mathrm{t}_{1}{ }^{\\prime}+\\vartheta x^{\\prime} \/ c^{2}}{\\sqrt{1-\\vartheta^{2} \/ c^{2}}}<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u2026 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 [1]<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u098f\u0996\u09a8 <span class=\"katex-eq\" data-katex-display=\"false\">t_0<\/span><\/span><span style=\"font-weight: 400;\"> \u09b8\u09ae\u09af\u09bc \u09aa\u09b0 \u099a-\u0995\u09be\u09a0\u09be\u09ae\u09cb\u09b0 \u09aa\u09b0\u09cd\u09af\u09ac\u09c7\u0995\u09cd\u09b7\u0995 \u09a6\u09c7\u0996\u09a4\u09c7 \u09aa\u09be\u09ac\u09c7 \u09a4\u09be\u09b0 \u0998\u09a1\u09bc\u09bf \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09b8\u09ae\u09af\u09bc <span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{t}_{2}'<\/span><\/span><span style=\"font-weight: 400;\">\u2019; \u0985\u09b0\u09cd\u09a5\u09be\u09ce <span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{t}_{0}=\\mathrm{t}_{2}{ }^{\\prime}-\\mathrm{t}_{1}{ }^{\\prime}\\mathrm{t}_{2}=\\frac{\\mathrm{t}_{2}{ }^{\\prime}+\\vartheta x^{\\prime} \/ c^{2}}{\\sqrt{1-\\vartheta^{2} \/ c^{2}}}<\/span><\/span><span style=\"font-weight: 400;\"> \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u0985\u099a-\u0995\u09be\u09a0\u09be\u09ae\u09cb\u09b0 \u09aa\u09b0\u09cd\u09af\u09ac\u09c7\u0995\u09cd\u09b7\u0995\u09c7\u09b0 \u09ae\u09a4\u09c7 \u09a4\u09be\u0981\u09b0 \u0998\u09a1\u09bc\u09bf \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09b8\u09ae\u09af\u09bc \u09b9\u09b2\u09cb <span class=\"katex-eq\" data-katex-display=\"false\">t_2<\/span>\u00a0<\/span><span style=\"font-weight: 400;\">\u00a0\u098f\u09ac\u0982<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{t}_{2}=\\frac{\\mathrm{t}_{2}{ }^{\\prime}+\\vartheta x^{\\prime} \/ c^{2}}{\\sqrt{1-\\vartheta^{2} \/ c^{2}}}<\/span> \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 [2]<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u098f\u0987 \u09aa\u09b0\u09cd\u09af\u09ac\u09c7\u0995\u09cd\u09b7\u0995\u09c7\u09b0 \u0995\u09be\u099b\u09c7 \u0998\u099f\u09a8\u09be\u09b0 \u09b8\u09ae\u09af\u09bc \u0995\u09be\u09b2<\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{t}=\\mathrm{t}_{2}-\\mathrm{t}_{1}=\\frac{\\mathrm{t}_{2}{ }^{\\prime}-\\mathrm{t}_{1}{ }^{\\prime}}{\\sqrt{1-\\vartheta^{2} \/ c^{2}}}<\/span>\n<p><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{c}\n\n=\\frac{\\mathrm{t}_{0}}{\\sqrt{1-\\vartheta^{2} \/ c^{2}}} \\\\\n\n\\therefore \\mathrm{t}_{0}=\\mathrm{t} \\sqrt{1-\\vartheta^{2} \/ c^{2}}\n\n\\end{array}<\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026\u00a0 \u00a0 \u00a0 \u00a0 [3]<\/p>\n<p><span style=\"font-weight: 400;\">\u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (3) \u09b9\u09a4\u09c7 \u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u09bf\u09a4 \u09b9\u09af\u09bc \u09af\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">t &gt; t_0<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u0985\u09b0\u09cd\u09a5\u09be\u09ce \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u0995\u09be\u09a0\u09be\u09ae\u09cb\u09a4\u09c7 \u09b8\u09ae\u09af\u09bc \u09a6\u09c0\u09b0\u09cd\u0998 \u09b9\u09af\u09bc\u0964 \u098f\u0995\u09c7 \u09b8\u09ae\u09af\u09bc \u09aa\u09cd\u09b0\u09b8\u09be\u09b0\u09a3 (Time dilation) \u09ac\u09b2\u09c7\u0964<\/span><\/p>\n<p><b>\u09b8\u09bf\u09a6\u09cd\u09ac\u09be\u09a8\u09cd\u09a4\u0983 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u0985\u09ac\u09a5\u09be\u09af\u09bc \u09a5\u09be\u0995\u09be \u0998\u09a1\u09bc\u09bf \u09a8\u09bf\u09b6\u09cd\u099a\u09b2 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09af\u09bc \u09a5\u09be\u0995\u09be \u0998\u09a1\u09bc\u09bf\u09b0 \u099a\u09c7\u09af\u09bc\u09c7 \u09a7\u09c0\u09b0\u09c7 \u099a\u09b2\u09c7\u0964 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09af\u09bc \u09a5\u09be\u0995\u09be \u0998\u09a1\u09bc\u09bf\u09b0 \u09b8\u09ae\u09af\u09bc \u09b8\u09bf\u09a5\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09af\u09bc \u09a5\u09be\u0995\u09be \u0998\u09a1\u09bc\u09bf\u09b0 \u099a\u09c7\u09af\u09bc\u09c7 <\/b><span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt{1-\\frac{v^{2}}{c^{2}}}<\/span><b>\u00a0\u09aa\u09b0\u09bf\u09ae\u09be\u09a3 \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf \u09aa\u09be\u09ac\u09c7\u0964<\/b><\/p>\n<h2><b>\u0986\u09aa\u09c7\u0995\u09cd\u09b7\u09bf\u0995\u09a4\u09be \u09a4\u09a4\u09cd\u09a4\u09cd\u09ac \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09b8\u0982\u0995\u09cb\u099a\u09a8 <\/b><b>(Length contraction according to the theory of relativity<\/b><b>)<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">\u099a\u09bf\u09b0\u09be\u09af\u09bc\u09a4 \u09ac\u09b2\u09ac\u09bf\u09a6\u09cd\u09af\u09be \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u09aa\u09b0\u09cd\u09af\u09ac\u09c7\u0995\u09cd\u09b7\u0995\u09c7\u09b0 \u09ac\u09c7\u0997 \u09ac\u09be \u09aa\u09b0\u09cd\u09af\u09ac\u09c7\u0995\u09cd\u09b7\u0995\u09c7\u09b0 \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09ac\u09c7\u0997 \u09af\u09be\u0987 \u09b9\u09cb\u0995 \u09a8\u09be \u0995\u09c7\u09a8, \u09b8\u0995\u09b2 \u09aa\u09b0\u09cd\u09af\u09ac\u09c7\u0995\u09cd\u09b7\u0995\u09c7\u09b0 \u09a8\u09bf\u0995\u099f \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u098f\u0995\u0987 \u09a5\u09be\u0995\u09c7\u0964 \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u0986\u09aa\u09c7\u0995\u09cd\u09b7\u09bf\u0995 \u09a4\u09a4\u09cd\u09a4\u09cd\u09ac \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09ac\u09b8\u09cd\u09a4\u09c1 \u0993 \u09aa\u09b0\u09cd\u09af\u09ac\u09c7\u0995\u09cd\u09b7\u0995\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u0986\u09aa\u09c7\u0995\u09cd\u09b7\u09bf\u0995 \u09ac\u09c7\u0997 \u09a5\u09be\u0995\u09b2\u09c7 \u09ac\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09aa\u09b0\u09cd\u09af\u09ac\u09c7\u0995\u09cd\u09b7\u0995\u09c7\u09b0 \u0995\u09be\u099b\u09c7 \u0995\u09ae \u09ac\u09b2\u09c7 \u09ae\u09a8\u09c7 \u09b9\u09af\u09bc\u0964 \u098f\u0995\u09c7 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09b8\u0982\u0995\u09cb\u099a\u09a8 (<\/span>Length contraction)<span style=\"font-weight: 400;\">\u09ac\u09b2\u09c7\u0964<\/span><\/p>\n<p><b>\u09aa\u09b0\u09cd\u09af\u09ac\u09c7\u0995\u09cd\u09b7\u0995\u09c7\u09b0 \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u0995\u09cb\u09a8\u09cb \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af, \u0993\u0987 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09b8\u09cd\u09a5\u09bf\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af\u09c7\u09b0 \u099a\u09c7\u09af\u09bc\u09c7 \u099b\u09cb\u099f \u09b9\u09af\u09bc \u098f\u09ac\u0982 \u098f\u0987 \u09aa\u09cd\u09b0\u09ad\u09be\u09ac\u0995\u09c7 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09b8\u0982\u0995\u09cb\u099a\u09a8 <span style=\"font-weight: 400;\">(<\/span>Length contraction) \u09ac\u09b2\u09c7\u0964<\/b><\/p>\n<h3><b>\u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09b8\u0999\u09cd\u0995\u09cb\u099a\u09a8 \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc (Calculating Length Contraction):<\/b><\/h3>\n<p><span style=\"font-weight: 400;\">\u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf \u0995\u09cb\u09a8\u09cb \u098f\u0995\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09a6\u09c1\u0987 \u09aa\u09cd\u09b0\u09be\u09a8\u09cd\u09a4\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09b0\u09cd\u09a4\u09c0 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac\u0987 \u09a4\u09be\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af\u0964 \u098f\u0996\u09a8 \u09a6\u09c1\u099f\u09bf \u0995\u09be\u09a0\u09be\u09ae\u09cb \u09ac\u09bf\u09ac\u09c7\u099a\u09a8\u09be \u0995\u09b0\u09bf\u0964 \u098f\u0995\u099f\u09bf S \u0995\u09be\u09a0\u09be\u09ae\u09cb, \u0985\u09aa\u09b0\u099f\u09bf S\u2019 \u0995\u09be\u09a0\u09be\u09ae\u09cb\u0964 \u098f\u0996\u09be\u09a8\u09c7 S \u0995\u09be\u09a0\u09be\u09ae\u09cb \u09b8\u09cd\u09a5\u09bf\u09b0\u0964 \u098f\u0995\u09c7 \u0985\u099a \u09a6\u09bf\u09af\u09bc\u09c7 \u09b8\u09c2\u099a\u09bf\u09a4 \u0995\u09b0\u09bf \u098f\u09ac\u0982 S&#8217; \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u0995\u09be\u09a0\u09be\u09ae\u09cb\u0964 \u098f\u0995\u09c7 \u099a \u09a6\u09bf\u09af\u09bc\u09c7 \u09b8\u09c2\u099a\u09bf\u09a4 \u0995\u09b0\u09bf\u0964 \u09b8\u09cd\u09a5\u09bf\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09af\u09bc AB \u09a6\u09a3\u09cd\u09a1 \u09ac\u09bf\u09ac\u09c7\u099a\u09a8\u09be \u0995\u09b0\u09bf\u0964<\/span><\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-9231 size-full\" src=\"https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/14.1-8.png\" alt=\"length contraction\" width=\"1052\" height=\"667\" srcset=\"https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/14.1-8.png 1052w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/14.1-8-300x190.png 300w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/14.1-8-1024x649.png 1024w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/14.1-8-768x487.png 768w\" sizes=\"(max-width: 1052px) 100vw, 1052px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p><span style=\"font-weight: 400;\">\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf \u0985\u099a \u0995\u09be\u09a0\u09be\u09ae\u09cb\u09b0 X \u0985\u0995\u09cd\u09b7 \u09ac\u09b0\u09be\u09ac\u09b0 \u098f\u0995\u099f\u09bf \u09a6\u09a3\u09cd\u09a1 \u09b6\u09be\u09af\u09bc\u09bf\u09a4 \u0986\u099b\u09c7\u0964 \u098f\u0987 \u0995\u09be\u09a0\u09be\u09ae\u09cb\u09b0 \u0995\u09cb\u09a8\u09cb \u09aa\u09b0\u09cd\u09af\u09ac\u09c7\u0995\u09cd\u09b7\u0995 \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u09b8\u09ae\u09af\u09bc\u09c7 \u09a6\u09c1\u0987 \u09aa\u09cd\u09b0\u09be\u09a8\u09cd\u09a4\u09c7\u09b0 \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995 \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0\u09b2 <span class=\"katex-eq\" data-katex-display=\"false\">x_1<\/span> <\/span><span style=\"font-weight: 400;\">\u00a0\u098f\u09ac\u0982 <span class=\"katex-eq\" data-katex-display=\"false\">x_2<\/span> <\/span><span style=\"font-weight: 400;\">\u0964 \u09a4\u09be\u09b0 \u09ae\u09a4\u09c7 \u09a6\u09a3\u09cd\u09a1\u099f\u09bf\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af <span class=\"katex-eq\" data-katex-display=\"false\">L_0=(x_2- x_1)<\/span><\/span><span style=\"font-weight: 400;\">\u0964 \u098f\u0987 <\/span><span style=\"font-weight: 400;\">\u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09a6\u09a3\u09cd\u09a1\u09c7\u09b0 \u09aa\u09cd\u09b0\u0995\u09c3\u09a4 \u098f\u09ac\u0982 \u09b8\u09cd\u09ac\u0995\u09c0\u09af\u09bc \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09aa\u09b0\u09cd\u09af\u09ac\u09c7\u0995\u09cd\u09b7\u0995 \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u09b8\u09cd\u09a5\u09bf\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09af\u09bc \u09aa\u09cd\u09b0\u09be\u09aa\u09cd\u09a4 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af\u0964 \u099a-\u0995\u09be\u09a0\u09be\u09ae\u09cb \u0985\u099a-\u0995\u09be\u09a0\u09be\u09ae\u09cb\u09b0 \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">\\vartheta<\/span> <\/span><span style=\"font-weight: 400;\">\u09ac\u09c7\u0997\u09c7 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u098f\u09ac\u0982 \u098f\u0987 \u0995\u09be\u09a0\u09be\u09ae\u09cb\u09b0 \u098f\u0995\u099c\u09a8 \u09aa\u09b0\u09cd\u09af\u09ac\u09c7\u0995\u09cd\u09b7\u0995 \u098f\u0995\u0987 \u09b8\u09ae\u09af\u09bc\u09c7 \u09a6\u09a3\u09cd\u09a1\u09c7\u09b0 \u09aa\u09cd\u09b0\u09be\u09a8\u09cd\u09a4 \u09a6\u09c1\u099f\u09bf\u09b0 \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u0999\u09cd\u0995 \u09a8\u09bf\u09b0\u09cd\u09a3\u09af\u09bc \u0995\u09b0\u09b2\u09c7\u09a8 <span class=\"katex-eq\" data-katex-display=\"false\">x_{1}^{\\prime}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u098f\u09ac\u0982 <span class=\"katex-eq\" data-katex-display=\"false\">x_{2}^{\\prime} \\mid<\/span> <\/span><span style=\"font-weight: 400;\">\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09a4\u09be\u0981\u09b0 \u09ae\u09be\u09aa\u09c7 \u09a6\u09a3\u09cd\u09a1\u09c7\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af,<span class=\"katex-eq\" data-katex-display=\"false\">L=\\left(x_{2}^{\\prime}-x_{1}^{\\prime}\\right)<\/span><\/span><span style=\"font-weight: 400;\">\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0985\u09a4\u098f\u09ac \u09b2\u09b0\u09c7\u099e\u09cd\u099c-\u098f\u09b0 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u09b0\u09c2\u09aa\u09be\u09a8\u09cd\u09a4\u09b0 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7,<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">x_{2}=\\frac{x_{2}{ }^{\\prime}+\\vartheta t}{\\sqrt{1-\\vartheta^{2} \/ c^{2}}}<\/span>\u00a0 \u00a0 \u00a0\u2026 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 [4]<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">x_{1}=\\frac{x_{1}{ }^{\\prime}+\\vartheta t}{\\sqrt{1-\\vartheta^{2} \/ c^{2}}}<\/span>\u00a0 \u00a0 \u00a0 \u2026 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 [5]<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u098f\u0996\u09a8 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (4) \u09b9\u09a4\u09c7 (5)-\u0995\u09c7 \u09ac\u09bf\u09df\u09cb\u0997 \u0995\u09b0\u09c7 \u09aa\u09be\u0987,\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{x}_{2}-\\mathrm{x}_{1}=\\frac{\\mathrm{x}_{2}^{\\prime}-\\mathrm{x}_{1}^{\\prime}}{\\sqrt{1-\\vartheta^{2} \/ c^{2}}}<\/span>\u00a0 \u00a0 \u00a0 \u2026 \u00a0 \u00a0 \u00a0 \u2026 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 [6]<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0986\u09ac\u09be\u09b0, <span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{L}_{0}=\\frac{L}{\\sqrt{1-\\vartheta^{2} \/ c^{2}}}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0 \u00a0 \u00a0\u2026 \u00a0 \u00a0 \u00a0 \u2026\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 [7]<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09ac\u09be, <span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{L}=\\mathrm{L}_{0} \\sqrt{1-\\vartheta^{2} \/ c^{2}}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0 \u00a0 \u2026 \u00a0 \u00a0 \u00a0 \u00a0 \u2026\u00a0 \u00a0 \u00a0 \u00a0 [8]<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (8) \u09b9\u09a4\u09c7 \u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u09bf\u09a4 \u09b9\u09df \u09af\u09c7, <span class=\"katex-eq\" data-katex-display=\"false\">L_0 &gt; L<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u0985\u09b0\u09cd\u09a5\u09be\u09ce \u0995\u09cb\u09a8\u09cb \u09a6\u09a3\u09cd\u09a1\u09c7\u09b0 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09a6\u09a3\u09cd\u09a1\u099f\u09bf\u09b0 \u09a8\u09bf\u09b6\u09cd\u099a\u09b2 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u098f\u09b0 \u099a\u09c7\u09df\u09c7 \u099b\u09cb\u099f \u09b9\u09ac\u09c7\u0964 \u098f\u0987 \u0998\u099f\u09a8\u09be\u0995\u09c7 \u09ac\u09b2\u09be \u09b9\u09df <strong>\u09b2\u09b0\u09c7\u099e\u09cd\u099c \u09ab\u09bf\u099f\u099c\u09c7\u09b0\u09be\u09b2\u09cd\u09a1 \u09b8\u0982\u0995\u09cb\u099a\u09a8 (Lorentz-Fitz Gerald contraction)<\/strong>\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0985\u09a4\u098f\u09ac <span class=\"katex-eq\" data-katex-display=\"false\">S'<\/span> \u0995\u09be\u09a0\u09be\u09ae\u09cb\u09b0 \u0995\u09cb\u09a8\u09cb \u09aa\u09b0\u09cd\u09af\u09ac\u09c7\u0995\u09cd\u09b7\u0995\u09c7\u09b0 \u09a8\u09bf\u0995\u099f S\u2019 \u0995\u09be\u09a0\u09be\u09ae\u09cb\u09a4\u09c7 \u09a6\u09a3\u09cd\u09a1\u09c7\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af <span class=\"katex-eq\" data-katex-display=\"false\">\\sqrt{1-\\vartheta^{2} \/ c^{2}}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09aa\u09b0\u09bf\u09ae\u09be\u09a3 \u099b\u09cb\u099f \u09ae\u09a8\u09c7 \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>\u098f\u0995\u099f\u09bf \u0995\u09be\u09b2\u09cd\u09aa\u09a8\u09bf\u0995 \u099f\u09cd\u09b0\u09c7\u09a8 \u0995\u09a4 \u09a6\u09cd\u09b0\u09c1\u09a4\u09bf\u09a4\u09c7 \u099a\u09b2\u09b2\u09c7 \u098f\u09b0 \u099a\u09b2\u09ae\u09be\u09a8 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09a8\u09bf\u09b6\u09cd\u099a\u09b2 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u098f\u09b0 \u098f\u0995-\u09a4\u09c3\u09a4\u09c0\u09df\u09be\u0982\u09b6 \u09b9\u09ac\u09c7?\u00a0<\/b><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">\u098f\u0996\u09be\u09a8\u09c7,\u00a0<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0995\u09be\u09b2\u09cd\u09aa\u09a8\u09bf\u0995 \u099f\u09cd\u09b0\u09c7\u09a8 \u098f\u09b0 \u09aa\u09cd\u09b0\u0995\u09c3\u09a4 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af = <span class=\"katex-eq\" data-katex-display=\"false\">L_0<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0995\u09be\u09b2\u09cd\u09aa\u09a8\u09bf\u0995 \u099f\u09cd\u09b0\u09c7\u09a8 \u098f\u09b0 \u099a\u09b2\u09ae\u09be\u09a8 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af = <span class=\"katex-eq\" data-katex-display=\"false\">L<\/span><\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\frac{\\mathrm{L}}{\\mathrm{L}_{0}}=\\frac{1}{3}<\/span>\n<span class=\"katex-eq\" data-katex-display=\"false\">C=3 \\times 10^{8} \\mathrm{~ms}^{-1}<\/span>\n<p><span style=\"font-weight: 400;\">\u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf,<\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{L}=\\mathrm{L}_{0} \\sqrt{1-\\vartheta^{2} \/ c^{2}}<\/span>\n<p><span style=\"font-weight: 400;\">\u09ac\u09be, <span class=\"katex-eq\" data-katex-display=\"false\">\\frac{\\mathrm{L}}{\\mathrm{L}_{0}}=\\sqrt{1-\\vartheta^{2} \/ \\mathrm{c}^{2}}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09aa\u09cd\u09b0\u09b6\u09cd\u09a8\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7, <span class=\"katex-eq\" data-katex-display=\"false\">\\frac{1}{3}=\\sqrt{1-\\vartheta^{2} \/ c^{2}}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09ac\u09be, <span class=\"katex-eq\" data-katex-display=\"false\">\\frac{1}{9}=1-\\vartheta^{2} \/ c^{2}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09ac\u09be, <span class=\"katex-eq\" data-katex-display=\"false\">\\frac{\\vartheta^{2}}{c^{2}}=1-\\frac{1}{9}=\\frac{8}{9}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09ac\u09be, <span class=\"katex-eq\" data-katex-display=\"false\">\\vartheta^{2}=\\frac{8}{9} c^{2}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\therefore \\vartheta=\\sqrt{\\frac{8}{9} \\times c^{2}}=\\sqrt{\\frac{8}{9} \\times\\left(3 \\times 10^{8}\\right)^{2}}<\/span><\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">2.83 \\times 10^8 ms^-1<\/span>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>\u098f\u0995\u099f\u09bf \u09ae\u09b9\u09be\u09b6\u09c2\u09a8\u09cd\u09af\u09af\u09be\u09a8 \u0995\u09a4 \u09a6\u09cd\u09b0\u09c1\u09a4 \u09ad\u09cd\u09b0\u09ae\u09a3 \u0995\u09b0\u09b2\u09c7 \u09ae\u09b9\u09be\u09b6\u09c2\u09a8\u09cd\u09af\u09c7 1 \u09a6\u09bf\u09a8 \u0985\u09a4\u09bf\u09ac\u09be\u09b9\u09bf\u09a4 \u09b9\u09b2\u09c7 \u09aa\u09c3\u09a5\u09bf\u09ac\u09c0\u09a4\u09c7 2 \u09a6\u09bf\u09a8 \u0985\u09a4\u09bf\u09ac\u09be\u09b9\u09bf\u09a4 \u09b9\u0993\u09df\u09be\u09b0 \u09b8\u09ae\u09be\u09a8 \u09b9\u09ac\u09c7?\u00a0<\/b><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">\u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf,<\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{l}\n\n\\mathrm{t}=\\frac{\\mathrm{t}_{0}}{\\sqrt{1-\\vartheta^{2} \/ c^{2}}} \\\\\n\n\\text { \u09ac\u09be, } 2=\\frac{1}{\\sqrt{1-\\vartheta^{2} \/ c^{2}}} \\\\\n\n\\text { \u09ac\u09be, } \\frac{1}{2}=\\sqrt{1-\\vartheta^{2} \/ c^{2}} \\\\\n\n\\text { \u09ac\u09be, } \\frac{1}{4}=1-\\vartheta^{2} \/ c^{2} \\\\\n\n\\text { \u09ac\u09be, } \\frac{\\vartheta^{2}}{c^{2}}=\\frac{3}{4} \\\\\n\n\\therefore \\vartheta=\\sqrt{\\frac{3}{4} \\times c^{2}}=0.866 \\times 3 \\times 10^{8} \\mathrm{~ms}^{-1} \\\\\n\n=2.598 \\times 10^{8} \\mathrm{~ms}^{-1}\n\n\\end{array}<\/span>\n<h2><b>\u09ad\u09b0 \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf (\u0986\u09aa\u09c7\u0995\u09cd\u09b7\u09bf\u0995\u09a4\u09be \u09a4\u09a4\u09cd\u09a4\u09cd\u09ac \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7) [<\/b><b>Increase of mass<\/b><b> (<\/b><b>according to the theory of relativity<\/b><b>)]<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">\u09a8\u09bf\u0989\u099f\u09a8\u09c0\u09af\u09bc \u09ac\u09b2\u09ac\u09bf\u09a6\u09cd\u09af\u09be\u09af\u09bc \u0986\u09ae\u09b0\u09be \u099c\u09c7\u09a8\u09c7\u099b\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09ad\u09b0 \u09a7\u09cd\u09b0\u09c1\u09ac \u09b0\u09be\u09b6\u09bf\u0964 \u09b8\u09cd\u09a5\u09be\u09a8, \u0995\u09be\u09b2 \u0993 \u0997\u09a4\u09bf\u09b0 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8\u09c7\u09b0 \u0993\u09aa\u09b0 \u098f\u099f\u09bf \u09a8\u09bf\u09b0\u09cd\u09ad\u09b0\u09b6\u09c0\u09b2 \u09a8\u09af\u09bc\u0964 \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u0986\u0987\u09a8\u09b8\u09cd\u099f\u09be\u0987\u09a8\u09c7\u09b0 \u0986\u09aa\u09c7\u0995\u09cd\u09b7\u09bf\u0995 \u09a4\u09a4\u09cd\u09a4\u09cd\u09ac\u09c7\u09b0 \u09ae\u09a4\u09c7 \u09a6\u09c8\u09f0\u09cd\u09af\u09cd\u09af \u0993 \u09b8\u09ae\u09af\u09bc\u09c7\u09b0 \u09ae\u09a4\u09cb \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09ad\u09b0\u0993 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2\u09a4\u09be\u09b0 \u0993\u09aa\u09b0 \u09a8\u09bf\u09b0\u09cd\u09ad\u09b0\u09b6\u09c0\u09b2\u0964 <\/span><b>\u0986\u09aa\u09c7\u0995\u09cd\u09b7\u09bf\u0995 \u09a4\u09a4\u09cd\u09a4\u09cd\u09ac\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09ac\u09c7\u0997\u09c7\u09b0 \u09b8\u09be\u09a5\u09c7 \u09ad\u09b0 \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf \u09aa\u09be\u09af\u09bc\u0964 \u098f \u0998\u099f\u09a8\u09be\u0995\u09c7 \u09ad\u09b0\u09c7\u09b0 \u0986\u09aa\u09c7\u0995\u09cd\u09b7\u09bf\u0995\u09a4\u09be \u09ac\u09b2\u09c7\u0964<\/b><\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-9232 size-full\" src=\"https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/16.1-4.png\" alt=\"increase of mass\" width=\"1052\" height=\"667\" srcset=\"https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/16.1-4.png 1052w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/16.1-4-300x190.png 300w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/16.1-4-1024x649.png 1024w, https:\/\/10minuteschool.com\/content\/wp-content\/uploads\/2021\/12\/16.1-4-768x487.png 768w\" sizes=\"(max-width: 1052px) 100vw, 1052px\" \/><\/p>\n<p><span style=\"font-weight: 400;\"><strong>\u09ac\u09cd\u09af\u09be\u0996\u09cd\u09af\u09be:<\/strong> \u09ae\u09a8\u09c7 \u0995\u09b0\u09bf S \u098f\u09ac\u0982 S&#8217; \u09a6\u09c1\u099f\u09bf \u099c\u09a1\u09bc \u09aa\u09cd\u09b0\u09b8\u0999\u09cd\u0997 \u0995\u09be\u09a0\u09be\u09ae\u09cb\u0964 S\u2019 \u0995\u09be\u09a0\u09be\u09ae\u09cb\u099f\u09bf x-\u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u0985\u09ad\u09bf\u09ae\u09c1\u0996\u09c7 S \u0995\u09be\u09a0\u09be\u09ae\u09cb\u09b0 \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 <\/span><span style=\"font-weight: 400;\"> \u09ac\u09c7\u0997\u09c7 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2\u0964 \u0995\u09be\u09a0\u09be\u09ae\u09cb\u0997\u09c1\u09b2\u09cb\u09a4\u09c7 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4 \u09a6\u09c1\u2019\u099c\u09a8 \u09aa\u09b0\u09cd\u09af\u09ac\u09c7\u0995\u09cd\u09b7\u0995 \u09a6\u09c1\u099f\u09bf \u0995\u09a3\u09be A \u0993 B \u098f\u09b0 \u09b8\u09cd\u09a5\u09bf\u09a4\u09bf\u09b8\u09cd\u09a5\u09be\u09aa\u0995 \u09b8\u0982\u0998\u09b0\u09cd\u09b7 \u09aa\u09b0\u09cd\u09af\u09ac\u09c7\u0995\u09cd\u09b7\u09a3 \u0995\u09b0\u099b\u09c7\u09a8\u0964 [\u0989\u09b2\u09cd\u09b2\u09c7\u0996\u09cd\u09af, \u09b8\u09cd\u09a5\u09bf\u09a4\u09bf\u09b8\u09cd\u09a5\u09be\u09aa\u0995 \u09b8\u0982\u0998\u09b0\u09cd\u09b7\u09c7 \u0997\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf \u09b8\u0982\u09b0\u0995\u09cd\u09b7\u09bf\u09a4 \u09a5\u09be\u0995\u09c7]\u0964 \u0995\u09a3\u09be \u09a6\u09c1\u099f\u09bf\u09b0 \u09ad\u09b0 \u09b8\u09ae\u09be\u09a8\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09a7\u09b0\u09bf \u09b8\u0982\u0998\u09b0\u09cd\u09b7\u09c7\u09b0 \u09aa\u09c2\u09b0\u09cd\u09ac\u09c7 A \u0995\u09a3\u09be\u099f\u09bf S \u0995\u09be\u09a0\u09be\u09ae\u09cb\u09a4\u09c7 \u098f\u09ac\u0982 B \u0995\u09a3\u09be\u099f\u09bf S&#8217; \u0995\u09be\u09a0\u09be\u09ae\u09cb\u09a4\u09c7 \u09b8\u09cd\u09a5\u09bf\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09af\u09bc \u09b0\u09af\u09bc\u09c7\u099b\u09c7\u0964 \u098f\u0995\u0987 \u09ae\u09c1\u09b9\u09c1\u09b0\u09cd\u09a4\u09c7 A \u0995\u09a3\u09be\u099f\u09bf <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vartheta_{A}<\/span><\/span><span style=\"font-weight: 400;\"> \u09ac\u09c7\u0997\u09c7 +Y \u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 \u098f\u09ac\u0982 B \u0995\u09a3\u09be\u099f\u09bf <span class=\"katex-eq\" data-katex-display=\"false\">\\vartheta_{B}^{\\prime}<\/span><\/span><span style=\"font-weight: 400;\"> \u09ac\u09c7\u0997\u09c7 \u2013Y\u2019 \u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 \u09a8\u09bf\u0995\u09cd\u09b7\u09c7\u09aa \u0995\u09b0\u09be \u09b9\u09b2\u09cb\u0964 \u098f\u0996\u09be\u09a8\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">\\vartheta_{A}=\\vartheta_{B}{ }^{\\prime} \\mathrm{~}<\/span><\/span><span style=\"font-weight: 400;\">\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982, S\u2019 \u0995\u09be\u09a0\u09be\u09ae\u09cb\u09a4\u09c7 A \u0995\u09a3\u09be\u09b0 \u0986\u099a\u09b0\u09a3 S&#8217; \u09aa\u09cd\u09b0\u09b8\u0999\u09cd\u0997 \u0995\u09be\u09a0\u09be\u09ae\u09cb\u09a4\u09c7 B \u0995\u09a3\u09be\u09b0 \u0986\u099a\u09b0\u09a3 \u0985\u09ad\u09bf\u09a8\u09cd\u09a8\u0964 \u09b8\u0982\u0998\u09b0\u09cd\u09b7\u09c7\u09b0 \u09aa\u09b0 A \u0995\u09a3\u09be\u099f\u09bf \u2013Y-\u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">\\vartheta_{A}<\/span><\/span><span style=\"font-weight: 400;\"> \u09ac\u09c7\u0997\u09c7 \u098f\u09ac\u0982 B \u0995\u09a3\u09be\u099f\u09bf +Y\u2019-\u0985\u0995\u09cd\u09b7\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">\\vartheta_{B}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09ac\u09c7\u0997\u09c7 \u09ab\u09bf\u09b0\u09c7 \u0986\u09b8\u09c7\u0964 \u09a8\u09bf\u0995\u09cd\u09b7\u09c7\u09aa\u09c7\u09b0 \u09ae\u09c1\u09b9\u09c2\u09b0\u09cd\u09a4\u09c7 \u0995\u09a3\u09be \u09a6\u09c1\u099f\u09bf\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09b0\u09cd\u09a4\u09c0 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac y \u09b9\u09b2\u09c7 \u0989\u09ad\u09af\u09bc \u09aa\u09b0\u09cd\u09af\u09ac\u09c7\u0995\u09cd\u09b7\u0995 \u09a6\u09c7\u0996\u09ac\u09c7\u09a8 \u09af\u09c7 \u09b8\u0982\u0998\u09b0\u09cd\u09b7\u099f\u09bf <span class=\"katex-eq\" data-katex-display=\"false\">\\frac{1}{2}y<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09a6\u09c2\u09b0\u09c7 \u09b8\u0982\u0998\u099f\u09bf\u09a4 \u09b9\u099a\u09cd\u099b\u09c7\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982, \u0985\u099a-\u0995\u09be\u09a0\u09be\u09ae\u09cb\u09a4\u09c7 A-\u098f\u09b0 \u09ae\u09cb\u099f \u09af\u09be\u09a4\u09be\u09af\u09bc\u09be\u09a4\u09c7\u09b0 \u09b8\u09ae\u09af\u09bc<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{t}_{0}=\\frac{y}{\\vartheta_{\\Lambda}}<\/span>\u00a0 \u00a0 \u00a0\u2026 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 [9]<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u098f\u09ac\u0982 \u099a-\u0995\u09be\u09a0\u09be\u09ae\u09cb\u09a4\u09c7 B-\u098f\u09b0 \u09af\u09be\u09a4\u09be\u09af\u09bc\u09be\u09a4\u09c7\u09b0 \u09b8\u09ae\u09af\u09bc \u098f\u0995\u0987 \u09a5\u09be\u0995\u09ac\u09c7 \u0985\u09b0\u09cd\u09a5\u09be\u09ce,<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{t}_{0}=\\frac{y}{\\vartheta_{\\mathrm{B}^{\\prime}}}<\/span>\u00a0 \u00a0 \u00a0 \u00a0\u2026 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 [10]<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0985\u099a-\u0995\u09be\u09a0\u09be\u09ae\u09cb\u09a4\u09c7 \u09ad\u09b0\u09ac\u09c7\u0997 \u09b8\u0982\u09b0\u0995\u09cd\u09b7\u09bf\u09a4 \u09b9\u09b2\u09c7,<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{m}_{\\mathrm{A}} \\vartheta_{\\mathrm{A}}=\\mathrm{m}_{\\mathrm{B}} \\vartheta_{\\mathrm{B}}<\/span>\u00a0 \u00a0 \u2026 \u00a0 \u00a0 \u00a0 \u00a0 \u2026 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 [11]<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u098f\u0996\u09be\u09a8\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">m_A<\/span><\/span><span style=\"font-weight: 400;\"> \u0993 <span class=\"katex-eq\" data-katex-display=\"false\">m_B<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u098f\u09ac\u0982 <\/span><span style=\"font-weight: 400;\">A<\/span><span style=\"font-weight: 400;\"> \u0993 <\/span><span style=\"font-weight: 400;\">B<\/span><span style=\"font-weight: 400;\"> \u0985\u099a-\u0995\u09be\u09a0\u09be\u09ae\u09cb\u09a4\u09c7 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 A \u0993 B \u0995\u09a3\u09be\u09b0 \u09ad\u09b0 \u0993 \u09ac\u09c7\u0997\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0985\u099a-\u0995\u09be\u09a0\u09be\u09ae\u09cb\u09a4\u09c7 B-\u098f\u09b0 \u09ad\u09cd\u09b0\u09ae\u09a3\u0995\u09be\u09b2 t \u09b9\u09b2\u09c7,<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{t}=\\frac{y}{\\vartheta_{\\mathrm{B}}}<\/span>, \u09ac\u09be, <span class=\"katex-eq\" data-katex-display=\"false\">\\vartheta_{\\mathrm{B}}=\\frac{y}{t}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0 \u00a0 \u00a0 \u2026 \u00a0 \u00a0 \u00a0 \u00a0 \u2026\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 [12]<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09af\u09a6\u09bf\u0993 \u0989\u09ad\u09af\u09bc \u09aa\u09b0\u09cd\u09af\u09ac\u09c7\u0995\u09cd\u09b7\u0995\u0987 \u098f\u0995\u0987 \u0998\u099f\u09a8\u09be \u09a8\u09bf\u099c \u09a8\u09bf\u099c \u0995\u09be\u09a0\u09be\u09ae\u09cb\u09a4\u09c7 \u09aa\u09b0\u09cd\u09af\u09ac\u09c7\u0995\u09cd\u09b7\u09a3 \u0995\u09b0\u099b\u09c7\u09a8, \u09a4\u09ac\u09c1 \u0998\u099f\u09a8\u09be\u09b0 \u09b8\u09ae\u09af\u09bc\u09c7\u09b0 \u09aa\u09b0\u09bf\u09ae\u09be\u09a3 \u09b8\u09ae\u09cd\u09ac\u09a8\u09cd\u09a7\u09c7 \u098f\u0995\u09ae\u09a4 \u09b9\u09a4\u09c7 \u09aa\u09be\u09b0\u099b\u09c7\u09a8 \u09a8\u09be\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u099a-\u0995\u09be\u09a0\u09be\u09ae\u09cb\u09a4\u09c7 B-\u098f\u09b0 \u09ad\u09cd\u09b0\u09ae\u09a3\u0995\u09be\u09b2 <span class=\"katex-eq\" data-katex-display=\"false\">t_0<\/span><\/span><span style=\"font-weight: 400;\"> \u09b9\u09b2\u09c7 \u09a6\u09c0\u09b0\u09cd\u0998\u09be\u09df\u09a8 \u09a8\u09c0\u09a4\u09bf \u09b9\u09a4\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">t<\/span> \u098f\u09ac\u0982 <span class=\"katex-eq\" data-katex-display=\"false\">t_0<\/span><\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">\u00a0\u09ae\u09a7\u09cd\u09af\u09c7 \u09b9\u09a4\u09c7 \u0986\u09ae\u09b0\u09be \u09af\u09c7 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995 \u09aa\u09be\u0987 \u09a4\u09be \u09b9\u09b2\u09cb,\u00a0<\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{t}=\\frac{t_{0}}{\\sqrt{1-\\vartheta^{2} \/ c^{2}}}<\/span>\n<p><span style=\"font-weight: 400;\">\u098f\u0996\u09a8 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (12)-\u098f t-\u098f\u09b0 \u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09df\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\vartheta_{\\mathrm{B}}=\\frac{y}{\\frac{t_{0}}{\\sqrt{1-\\vartheta^{2} \/ c^{2}}}}<\/span>\n<p><span style=\"font-weight: 400;\">\u09ac\u09be,<\/span><span style=\"font-weight: 400;\">\u00a0 \u00a0<span class=\"katex-eq\" data-katex-display=\"false\">\\vartheta_{\\mathrm{B}}=y \\sqrt{1-\\vartheta^{2} \/ c^{2}} \/ t_{0}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u098f\u0996\u09a8 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (9)-\u09b9\u09a4\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\vartheta_{\\mathrm{A}}=\\frac{y}{t_{0}}<\/span>\n<p><span style=\"font-weight: 400;\">\u2234<\/span><span style=\"font-weight: 400;\"> \u09ad\u09b0\u09ac\u09c7\u0997\u09c7\u09b0 \u09b8\u0982\u09b0\u0995\u09cd\u09b7\u09a3 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (11)-\u098f <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vartheta_{\\mathrm{A}}<\/span><\/span><span style=\"font-weight: 400;\"> \u0993 <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vartheta_{\\mathrm{B}}<\/span><\/span><span style=\"font-weight: 400;\">-\u098f\u09b0 \u09ae\u09be\u09a8 \u09ac\u09b8\u09bf\u09df\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n<p><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{l}\n\n\\mathrm{m}_{\\mathrm{A}} \\frac{y}{t_{0}}=\\mathrm{m}_{\\mathrm{B}} \\frac{y \\sqrt{1-\\vartheta^{2} \/ c^{2}}}{t_{0}} \\\\\n\n\\therefore \\mathrm{m}_{\\mathrm{A}}=\\mathrm{m}_{\\mathrm{B}} \\sqrt{1-\\vartheta^{2} \/ c^{2}}\n\n\\end{array}<\/span>\u00a0 \u00a0 \u00a0\u2026\u00a0 \u00a0 \u00a0 \u00a0 \u2026 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 [13]<\/p>\n<p><span style=\"font-weight: 400;\">\u09b8\u09c1\u09a4\u09b0\u09be\u0982, \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (13) \u09b9\u09a4\u09c7 \u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u09bf\u09a4 \u09b9\u09af\u09bc \u09af\u09c7,<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09b6\u09c1\u09b0\u09c1\u09a4\u09c7 \u0986\u09ae\u09b0\u09be \u09a7\u09b0\u09c7 \u09a8\u09bf\u09b2\u09be\u09ae \u09af\u09c7 \u0995\u09a3\u09be\u09af\u09bc \u098f\u0995\u0987\u09b0\u09c2\u09aa (identical), \u098f\u09a6\u09c7\u09b0 \u09ad\u09b0 \u09b8\u09ae\u09be\u09a8\u0964 \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (13) \u09a5\u09c7\u0995\u09c7 \u09a6\u09c7\u0996\u09be \u09af\u09be\u09af\u09bc, \u09a4\u09be \u09b8\u09a0\u09bf\u0995 \u09a8\u09af\u09bc\u0964 \u0985\u09b0\u09cd\u09a5\u09be\u09ce <span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{m}_{\\mathrm{A}} \\neq \\mathrm{m}_{\\mathrm{B}} \\mid<\/span><\/span><span style=\"font-weight: 400;\">\u0964 \u098f\u09b0 \u0985\u09b0\u09cd\u09a5 \u09b9\u09b2\u09cb, \u09b8\u09cd\u09a5\u09be\u09a8 \u0993 \u09b8\u09ae\u09af\u09bc\u09c7\u09b0 \u0985\u09a8\u09c1\u09b0\u09c2\u09aa \u09ad\u09b0\u09c7\u09b0 \u09aa\u09b0\u09bf\u09ae\u09be\u09aa\u0993 \u09aa\u09b0\u09cd\u09af\u09ac\u09c7\u0995\u09cd\u09b7\u0995 \u0993 \u09aa\u09b0\u09cd\u09af\u09ac\u09c7\u0995\u09cd\u09b7\u09a3\u09c0\u09af\u09bc \u09ac\u09b0 \u0986\u09aa\u09c7\u0995\u09cd\u09b7\u09bf\u0995 \u0997\u09a4\u09bf\u09b0 \u0989\u09aa\u09b0\u09c7 \u09a8\u09bf\u09b0\u09cd\u09ad\u09b0\u09b6\u09c0\u09b2\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0989\u09aa\u09b0\u09c7\u09b0 \u09a6\u09c3\u09b7\u09cd\u099f\u09be\u09a8\u09cd\u09a4\u09c7 A \u0993 B \u0995\u09a3\u09be\u09a6\u09cd\u09ac\u09df \u098f\u0995\u0987 \u09aa\u09cd\u09b0\u09b8\u0999\u09cd\u0997 \u0995\u09be\u09a0\u09be\u09ae\u09cb S-\u098f \u0997\u09a4\u09bf\u09b6\u09c0\u09b2\u0964 \u098f\u0996\u09a8 \u098f\u0995\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09af\u09bc \u09ad\u09b0 \u098f\u09ac\u0982 \u0993\u0987 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09a8\u09bf\u09b6\u09cd\u099a\u09b2 \u09ac\u09be \u09b8\u09cd\u09a5\u09bf\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09b0 \u09ad\u09b0 \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995\u09c0\u09af\u09bc \u09b8\u09c2\u09a4\u09cd\u09b0 \u09aa\u09cd\u09b0\u09be\u09aa\u09cd\u09a4\u09bf\u09b0 \u099c\u09a8\u09cd\u09af \u0993\u09aa\u09a4\u09cd\u09b0\u09c7\u09b0 \u09a6\u09c3\u09b7\u09cd\u099f\u09be\u09a8\u09cd\u09a4\u09c7\u09b0 \u0985\u09a8\u09c1\u09b0\u09c2\u09aa \u09a6\u09c3\u09b7\u09cd\u099f\u09be\u09a8\u09cd\u09a4 \u09ac\u09bf\u09ac\u09c7\u099a\u09a8\u09be \u0995\u09b0\u09be \u09af\u09c7\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7\u0964 \u098f\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 <\/span><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\vartheta_{\\mathrm{A}}<\/span><\/span><span style=\"font-weight: 400;\"> \u0993 <span class=\"katex-eq\" data-katex-display=\"false\">\\vartheta_{\\mathrm{B}}'<\/span><\/span><span style=\"font-weight: 400;\"> \u0996\u09c1\u09ac \u0995\u09ae \u09ae\u09be\u09a8\u09c7\u09b0 \u09b9\u09b2\u09c7 S \u09ac\u09be \u0985\u099a-\u0995\u09be\u09a0\u09be\u09ae\u09cb \u098f\u0995\u099c\u09a8 \u09aa\u09b0\u09cd\u09af\u09ac\u09c7\u0995\u09cd\u09b7\u0995 \u09a6\u09c7\u0996\u09ac\u09c7\u09a8 \u09af\u09c7 A \u09b8\u09cd\u09a5\u09bf\u09b0 \u09b0\u09af\u09bc\u09c7\u099b\u09c7 \u098f\u09ac\u0982 B, A \u098f\u09b0 \u09a6\u09bf\u0995\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">\\vartheta<\/span>\u00a0<\/span><span style=\"font-weight: 400;\"> \u09ac\u09c7\u0997\u09c7 \u0985\u0997\u09cd\u09b0\u09b8\u09b0 \u09b9\u09af\u09bc\u09c7 \u09ae\u09c1\u09b9\u09c2\u09b0\u09cd\u09a4\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09a4\u09bf\u09b0\u09cd\u09af\u0995\u09ad\u09be\u09ac\u09c7 \u09b8\u0982\u0998\u09b0\u09cd\u09b7 \u0998\u099f\u09bf\u09af\u09bc\u09c7 \u09a6\u09cd\u09b0\u09c1\u09a4 \u09b8\u09be\u09ae\u09a8\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 \u0985\u0997\u09cd\u09b0\u09b8\u09b0 \u09b9\u099a\u09cd\u099b\u09c7\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u2234<\/span><span style=\"font-weight: 400;\"> S (\u0985\u099a)-\u0995\u09be\u09a0\u09be\u09ae\u09cb\u0995\u09c7 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{m}_{\\mathrm{A}}=\\mathrm{m}_{0}=<\/span><\/span><span style=\"font-weight: 400;\"> \u0995\u09a3\u09be\u09b0 \u09b8\u09cd\u09a5\u09bf\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09af\u09bc \u09ad\u09b0 \u098f\u09ac\u0982 <span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{m}_{\\mathrm{B}}=\\mathrm{m}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0\u09a7\u09b0\u09be \u09b9\u09b2\u09c7, \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (13) \u09b9\u09a4\u09c7 \u09aa\u09be\u0987,<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{m}_{0}=\\mathrm{m} \\sqrt{1-\\vartheta^{2} \/ c^{2}}, \\mathrm{~m}_{0}=<\/span> \u09b8\u09cd\u09a5\u09bf\u09b0<\/span> <span style=\"font-weight: 400;\">\u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09b0 \u09ad\u09b0, m = \u099a\u09b2\u09ae\u09be\u09a8<\/span> <span style=\"font-weight: 400;\">\u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09b0 \u09ad\u09b0\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u09ac\u09be, <span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{m}=\\frac{\\mathrm{m}_{0}}{\\sqrt{1-\\vartheta^{2} \/ c^{2}}}=\\quad \\frac{\\mathrm{m}_{0}}{\\sqrt{1-\\beta^{2}}}<\/span><\/span><span style=\"font-weight: 400;\">\u00a0 \u00a0 \u00a0 \u00a0<\/span><span style=\"font-weight: 400;\">\u2026\u00a0 \u00a0 \u00a0 \u00a0 \u2026 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 [14]<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u098f\u0996\u09be\u09a8\u09c7, <span class=\"katex-eq\" data-katex-display=\"false\">\\beta^{2}=\\frac{\\vartheta^{2} }{c^{2}}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0986\u09ac\u09be\u09b0, \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 S&#8217; \u09ac\u09be \u099a-\u0995\u09be\u09a0\u09be\u09ae\u09cb\u09b0 \u098f\u0995\u099c\u09a8 \u09aa\u09b0\u09cd\u09af\u09ac\u09c7\u0995\u09cd\u09b7\u0995 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be \u09b2\u0995\u09cd\u09b7 \u0995\u09b0\u09ac\u09c7\u09a8\u0964 \u09a4\u09bf\u09a8\u09bf \u09a6\u09c7\u0996\u09ac\u09c7\u09a8, B \u09b8\u09cd\u09a5\u09bf\u09b0 \u09b0\u09af\u09bc\u09c7\u099b\u09c7 \u098f\u09ac\u0982 A \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf B \u098f\u09b0 \u09a6\u09bf\u0995\u09c7 <\/span><span style=\"font-weight: 400;\"> \u09ac\u09c7\u0997\u09c7 \u0985\u0997\u09cd\u09b0\u09b8\u09b0 \u09b9\u09af\u09bc\u09c7 \u09ae\u09c1\u09b9\u09c1\u09b0\u09cd\u09a4\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09a4\u09bf\u09b0\u09cd\u09af\u0995 \u09b8\u09cd\u09a4\u09b0\u09c7 \u09b8\u0982\u0998\u09b0\u09cd\u09b7 \u0998\u099f\u09bf\u09af\u09bc\u09c7 \u09b8\u09be\u09ae\u09a8\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 \u098f\u0997\u09bf\u09af\u09bc\u09c7 \u099a\u09b2\u09c7\u099b\u09c7\u0964 S \u098f\u09ac\u0982 S&#8217; \u0995\u09be\u09a0\u09be\u09ae\u09cb \u09a5\u09c7\u0995\u09c7 \u09b8\u0982\u0998\u09b0\u09cd\u09b7 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u099f\u09bf \u09aa\u09b0\u09cd\u09af\u09ac\u09c7\u0995\u09cd\u09b7\u09a3 \u0995\u09b0\u09b2\u09c7 \u0995\u09c0\u09b0\u09c2\u09aa \u09a6\u09c7\u0996\u09be \u09af\u09be\u09ac\u09c7, \u09a4\u09be \u099a\u09bf\u09a4\u09cd\u09b0 \u09ee.\u09ef-\u098f \u09a6\u09c7\u0996\u09be\u09a8\u09cb \u09b9\u09af\u09bc\u09c7\u099b\u09c7\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u0989\u09aa\u09b0\u09cb\u0995\u09cd\u09a4 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (14) \u09b9\u09a4\u09c7 \u09aa\u09cd\u09b0\u09ae\u09be\u09a3\u09bf\u09a4 \u09b9\u09af\u09bc \u09af\u09c7 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u0995\u09cb\u09a8\u09cb \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09ad\u09b0 \u0993\u0987 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09a8\u09bf\u09b6\u09cd\u099a\u09b2 \u09ad\u09b0\u09c7\u09b0 \u099a\u09c7\u09af\u09bc\u09c7 \u09ac\u09c7\u09b6\u09bf\u0964 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09ac\u09c7\u0997\u09c7\u09b0 \u09b8\u09be\u09a5\u09c7 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09ad\u09b0\u09ac\u09c3\u09a6\u09cd\u09a7\u09bf \u0998\u099f\u09c7\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><strong>\u0995\u09be\u099c\u0983<\/strong> \u0986\u09aa\u09c7\u0995\u09cd\u09b7\u09bf\u0995 \u09a4\u09a4\u09cd\u09a4\u09cd\u09ac\u09c7\u09b0 \u09b8\u09be\u09b9\u09be\u09af\u09cd\u09af\u09c7 \u09a6\u09c7\u0996\u09be\u0993 \u09af\u09c7, \u0995\u09cb\u09a8\u09cb \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09ac\u09c7\u0997 \u0986\u09b2\u09cb\u09b0 \u09ac\u09c7\u0997\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8 \u09b9\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7 \u09a8\u09be\u0964<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><em><strong>Hints:<\/strong><\/em> \u09ad\u09b0\u09c7\u09b0 \u0986\u09aa\u09c7\u0995\u09cd\u09b7\u09bf\u0995\u09a4\u09be \u09a5\u09c7\u0995\u09c7 \u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf, <span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{m}=\\frac{\\mathrm{m}_{0}}{\\sqrt{1-\\vartheta^{2} \/ c^{2}}}<\/span><\/span><\/p>\n<p><span style=\"font-weight: 400;\"> <span class=\"katex-eq\" data-katex-display=\"false\">\\vartheta=\\mathrm{c}<\/span> \u09b9\u09b2\u09c7, <span class=\"katex-eq\" data-katex-display=\"false\">\\mathrm{m}=\\frac{\\mathrm{m}_{0}}{\\sqrt{1-c^{2} \/ c^{2}}}=\\frac{\\mathrm{m}_{0}}{\\sqrt{1-1}}=\\frac{\\mathrm{m}_{0}}{0}=\\infty<\/span><\/span><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\">\u09b9\u09df, \u09af\u09be \u0985\u09b8\u09ae\u09cd\u09ad\u09ac\u0964 \u09a4\u09be\u0987 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09ac\u09c7\u0997 \u0986\u09b2\u09cb\u09b0 \u09ac\u09c7\u0997\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8 \u09ac\u09be \u09ac\u09c7\u09b6\u09bf \u09b9\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7 \u09a8\u09be\u0964<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>\u098f\u0995\u099f\u09bf \u0987\u09b2\u09c7\u0995\u099f\u09cd\u09b0\u09a8 <\/b><span style=\"font-weight: 400;\">0.99c<\/span><b> \u09a6\u09cd\u09b0\u09c1\u09a4\u09bf\u09a4\u09c7 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u09b9\u09b2\u09c7 \u098f\u09b0 \u099a\u09b2\u09ae\u09be\u09a8 \u09ad\u09b0 \u0995\u09a4?<\/b><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">\u098f\u0996\u09be\u09a8\u09c7,<\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{l}\n\n\\mathrm{m}_{0}=9.1 \\times 10^{-31} \\mathrm{~kg} \\\\\n\n\\vartheta=0.99 \\mathrm{c} \\\\\n\nm=?\n\n\\end{array}<\/span>\n<p><span style=\"font-weight: 400;\">\u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf,<\/span><\/p>\n<span class=\"katex-eq\" data-katex-display=\"false\">\\begin{aligned}\n\n\\mathrm{m} &amp;=\\frac{\\mathrm{m}_{0}}{\\sqrt{1-\\vartheta^{2} \/ c^{2}}}=\\frac{9.1 \\times 10^{-31}}{\\sqrt{1-(0.99)^{2} \\mathrm{c}^{2} \/ c^{2}}} \\\\\n\n&amp;=\\frac{9.1 \\times 10^{-31}}{\\sqrt{1-0.9801}}=\\frac{9.1 \\times 10^{-31}}{0.1410} \\\\\n\n&amp;=6.45 \\times 10^{-30} \\mathrm{~kg}\n\n\\end{aligned}<\/span>\n","protected":false},"excerpt":{"rendered":"<p>\u0986\u09aa\u09c7\u0995\u09cd\u09b7\u09bf\u0995\u09a4\u09be \u09a4\u09a4\u09cd\u09a4\u09cd\u09ac \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09b8\u09ae\u09af\u09bc \u09aa\u09cd\u09b0\u09b8\u09be\u09b0\u09a3 (Time dilation according to the theory of relativity) \u0995\u09cb\u09a8\u09cb \u099c\u09a1\u09bc \u09ac\u09be \u09b8\u09cd\u09a5\u09bf\u09b0 \u0995\u09be\u09a0\u09be\u09ae\u09cb\u09a4\u09c7 \u09b8\u0982\u0998\u099f\u09bf\u09a4 \u0998\u099f\u09a8\u09be \u0989\u0995\u09cd\u09a4 \u0995\u09be\u09a0\u09be\u09ae\u09cb \u09b8\u09be\u09aa\u09c7\u0995\u09cd\u09b7\u09c7 \u0997\u09a4\u09bf\u09b6\u09c0\u09b2 \u0985\u09a8\u09cd\u09af \u0995\u09cb\u09a8\u09cb \u0995\u09be\u09a0\u09be\u09ae\u09cb \u09a5\u09c7\u0995\u09c7 \u09b2\u0995\u09cd\u09b7\u09cd\u09af \u0995\u09b0\u09b2\u09c7 \u09a6\u09c7\u0996\u09be \u09af\u09be\u09ac\u09c7 \u0998\u099f\u09a8\u09be\u09b0 \u09b8\u09ae\u09af\u09bc \u09ac\u09cd\u09af\u09ac\u09a7\u09be\u09a8 \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf \u09aa\u09c7\u09af\u09bc\u09c7\u099b\u09c7\u0964 \u098f \u09ac\u09bf\u09b7\u09af\u09bc\u099f\u09bf\u0995\u09c7 \u09b8\u09ae\u09af\u09bc<\/p>\n<p> <a class=\"redmore\" href=\"https:\/\/10minuteschool.com\/content\/time-dilation-length-contraction\/\">Read More<\/a><\/p>\n","protected":false},"author":56,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[4252,3029,50,51],"tags":[2418,2417,2419,2416],"_links":{"self":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/3437"}],"collection":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/users\/56"}],"replies":[{"embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/comments?post=3437"}],"version-history":[{"count":13,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/3437\/revisions"}],"predecessor-version":[{"id":9233,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/3437\/revisions\/9233"}],"wp:attachment":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/media?parent=3437"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/categories?post=3437"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/tags?post=3437"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}