{"id":2903,"date":"2022-03-24T11:20:50","date_gmt":"2022-03-24T11:20:50","guid":{"rendered":"https:\/\/stage-wp.10minuteschool.com\/?p=2903"},"modified":"2022-03-24T05:43:35","modified_gmt":"2022-03-24T05:43:35","slug":"work-done-by-gravitational-force","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/work-done-by-gravitational-force\/","title":{"rendered":"\u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09c3\u09a4 \u0995\u09be\u099c(Work Done by Gravitational Force)"},"content":{"rendered":"

\u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2 <\/b>\\left(F \\propto \\frac{1}{r^{2}}\\right)<\/span><\/span>\u00a0\u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09c3\u09a4 \u0995\u09be\u099c(Work Done by Gravitational Force)<\/b><\/h2>\n

\u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf, \u098f \u09ae\u09b9\u09be\u09ac\u09bf\u09b6\u09cd\u09ac\u09c7\u09b0 \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u09a6\u09c1\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be \u098f\u0995\u09c7 \u0985\u09aa\u09b0\u0995\u09c7 \u098f\u0995\u099f\u09bf \u09ac\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u0995\u09b0\u09c7\u0964 \u098f \u09ac\u09b2\u0995\u09c7 \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2 \u09ac\u09b2\u09be \u09b9\u09af\u09bc\u0964 \u098f\u099f\u09bf \u098f\u0995\u099f\u09bf \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8\u09b6\u09c0\u09b2 \u09ac\u09b2<\/a>\u2014\u09a6\u09c1\u099f\u09bf \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u099c\u09a8\u09cd\u09af \u098f \u09ac\u09b2\u09c7\u09b0 \u09ae\u09be\u09a8 \u09a4\u09be\u09a6\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09b0\u09cd\u09a4\u09c0 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac\u09c7\u09b0 \u0989\u09aa\u09b0 \u09a8\u09bf\u09b0\u09cd\u09ad\u09b0 \u0995\u09b0\u09c7\u0964 \u09aa\u09cd\u09b0\u0995\u09c3\u09a4\u09aa\u0995\u09cd\u09b7\u09c7, \u098f \u09ac\u09b2 <\/span>(<\/span>F)<\/span> \u09ac\u09b8\u09cd\u09a4\u09c1\u09a6\u09cd\u09ac\u09af\u09bc\u09c7\u09b0 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac\u09c7\u09b0 \u09ac\u09b0\u09cd\u0997\u09c7\u09b0\\left(r^{2}\\right)<\/span><\/span>\u09ac\u09cd\u09af\u09b8\u09cd\u09a4\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09c7 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09bf\u09a4 \u09b9\u09af\u09bc, \u0985\u09b0\u09cd\u09a5\u09be\u09ce <\/span><\/p>\n

\\left(F \\propto \\frac{1}{r^{2}}\\right)<\/span>\u0964 \u098f\u0996\u09a8 \u0986\u09ae\u09b0\u09be \u098f\u0987 \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u0995\u09c3\u09a4 \u0995\u09be\u099c \u09b9\u09bf\u09b8\u09be\u09ac \u0995\u09b0\u09ac\u09cb<\/span>\u0964 <\/span>\u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf, <\/span>m<\/span><\/em> \u098f\u09ac\u0982 <\/span>M<\/span><\/em> \u09ad\u09b0\u09c7\u09b0 \u09a6\u09c1\u099f\u09bf \u0995\u09a3\u09be \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 \u09a5\u09c7\u0995\u09c7 <\/span>r<\/span> \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac\u09c7 \u09a5\u09be\u0995\u09b2\u09c7 \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09b8\u09c2\u09a4\u09cd\u09b0 \u0985\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09a4\u09be\u09a6\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09ac\u09b2,<\/span><\/p>\n\\left(F=-\\frac{G M m}{r^{2}}\\right)<\/span>\n

\u098f\u0996\u09be\u09a8\u09c7 \u098b\u09a3\u09be\u09a4\u09cd\u09ae\u0995 \u099a\u09bf\u09b9\u09cd\u09a8 \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u09ac\u09b2 \u09a8\u09bf\u09b0\u09cd\u09a6\u09c7\u09b6 \u0995\u09b0\u099b\u09c7\u0964<\/span><\/p>\n

\u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09c3\u09a4 \u0995\u09be\u099c\u09c7\u09b0 \u09b9\u09bf\u09b8\u09be\u09ac(Calculation of Work Done by Gravitational Force)<\/b><\/h2>\n

\u09a7\u09b0\u09be \u09af\u09be\u0995, \u0995\u09cb\u09a8\u09cb \u09b8\u09cd\u09a5\u09be\u09a8\u09c7 <\/span>P<\/span><\/em> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 <\/span>M<\/span><\/em> \u09ad\u09b0\u09c7\u09b0 \u098f\u0995\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4\u0964 <\/span>P<\/span><\/em> \u09a5\u09c7\u0995\u09c7 <\/span>r<\/span><\/em> \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac\u09c7 <\/span>Q<\/span><\/em> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 <\/span>m<\/span><\/em> \u09ad\u09b0\u09c7\u09b0 \u0986\u09b0\u09c7\u0995\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4 (\u099a\u09bf\u09a4\u09cd\u09b0)\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09b8\u09c2\u09a4\u09cd\u09b0\u09be\u09a8\u09c1\u09b8\u09be\u09b0\u09c7 \u09a4\u09be\u09a6\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u0995\u09be\u09b0 \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u09ac\u09b2,<\/span><\/p>\n

 <\/p>\nF=-G \\frac{M m}{r^{2}}<\/span>\n

m<\/span><\/em> \u09ad\u09b0\u09c7\u09b0 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0989\u09aa\u09b0 \u098f\u0987 \u09ac\u09b2 <\/span>QP<\/span> \u09ac\u09b0\u09be\u09ac\u09b0 \u0995\u09cd\u09b0\u09bf\u09af\u09bc\u09be\u09b6\u09c0\u09b2\u0964 \u098f\u0996\u09a8 <\/span>m<\/span><\/em> \u09ad\u09b0\u09c7\u09b0 \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf\u0995\u09c7 <\/span>Q<\/span><\/em> \u09a5\u09c7\u0995\u09c7 \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0\u09be\u09a4\u09bf\u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac d r<\/span><\/span>\u09b8\u09b0\u09bf\u09af\u09bc\u09c7 <\/span>R<\/span><\/em> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09a8\u09bf\u09a4\u09c7 \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09c3\u09a4 \u0995\u09be\u099c,<\/span><\/p>\nd W=F d r \\cos 0^{\\circ}<\/span>\n

=F d r<\/span><\/span><\/p>\n

\"gravitational-force\"<\/p>\n

\u09a7\u09b0\u09be \u09af\u09be\u0995, \u09ac\u09b8\u09cd\u09a4\u09c1 \u09a6\u09c1\u099f\u09bf\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u0986\u09a6\u09bf \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u099b\u09bf\u09b2 r_{a}<\/span><\/span>\u0964 <\/span>\u098f\u0996\u09a8 \u09a4\u09be\u09a6\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 <\/span>r_{b}<\/span><\/span> \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u09b8\u09c3\u09b7\u09cd\u099f\u09bf \u0995\u09b0\u09a4\u09c7 \u098f\u0987 \u09ac\u09b2\u09c7\u09b0 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09c3\u09a4 \u0995\u09be\u099c W_{a b}<\/span><\/span>, \u0989\u09aa\u09b0\u09bf\u0989\u0995\u09cd\u09a4 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u0995\u09c7 \u09af\u09cb\u0997\u099c\u09c0\u0995\u09b0\u09a3 \u0995\u09b0\u09b2\u09c7\u0987 \u09aa\u09be\u0993\u09af\u09bc\u09be \u09af\u09be\u09af\u09bc\u0964 \u098f\u0987 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u0995\u09c7 r=r_{a}<\/span><\/span>\u09a5\u09c7\u0995\u09c7 <\/span>r=r_{b}<\/span><\/span>\u00a0\u098f\u0987 \u09b8\u09c0\u09ae\u09be\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09af\u09cb\u0997\u099c\u09c0\u0995\u09b0\u09a3 \u0995\u09b0\u09c7 \u0986\u09ae\u09b0\u09be \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09c3\u09a4 \u0995\u09be\u099c \u09aa\u09be\u0987,<\/span><\/p>\n\\begin{array}{l}\n\nW_{a b}=\\int_{r_{a}}^{r_{b}} F d r=-\\int_{r_{a}}^{r_{b}} \\frac{G M m}{r^{2}} d r \\\\\n\n\\quad=-G M m \\int_{r_{a}}^{r_{b}} \\frac{d r}{r^{2}}=-G M m\\left[-\\frac{1}{r}\\right]_{r_{a}}^{r_{b}} \\\\\n\n\\therefore W_{a b}=G M m\\left(\\frac{1}{r_{b}}-\\frac{1}{r_{a}}\\right)\n\n\\end{array}<\/span>\n

\u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09c3\u09a4 \u09a7\u09a8\u09be\u09a4\u09cd\u09ae\u0995 \u0995\u09be\u099c(Positive Work Done by Gravitational Force)<\/b><\/h2>\n

\u09b8\u09ae\u09c0\u0995\u09b0\u09a3 \u09a5\u09c7\u0995\u09c7 \u09a6\u09c7\u0996\u09be \u09af\u09be\u09af\u09bc \u09af\u09c7, \u09a6\u09c1\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1 \u0995\u09a3\u09be\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u09b9\u09cd\u09b0\u09be\u09b8 \u0995\u09b0\u09be \u09b9\u09b2\u09c7 \u0985\u09b0\u09cd\u09a5\u09be\u09ce r_{b}<r_{a}<\/span><\/span> \u09b9\u09b2\u09c7 \\frac{1}{r_{b}}><\/span>\\frac{1}{r_{a}}<\/span><\/span> \u09b9\u09df, \u09ab\u09b2\u09c7 W_{a b}<\/span><\/span>\u00a0\u09a7\u09a8\u09be\u09a4\u09cd\u09ae\u0995 \u09b9\u09af\u09bc; \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2 \u09a7\u09a8\u09be\u09a4\u09cd\u09ae\u0995 \u0995\u09be\u099c \u09b8\u09ae\u09cd\u09aa\u09a8\u09cd\u09a8 \u0995\u09b0\u09c7\u0964 \u09af\u09c7\u09ae\u09a8 \u0986\u09ae\u09b0\u09be \u09af\u09a6\u09bf \u0989\u09aa\u09b0 \u09a5\u09c7\u0995\u09c7 \u098f\u0995\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1 \u099b\u09c7\u09dc\u09c7 \u09a6\u09c7\u0987, \u098f\u099f\u09bf \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2\u09c7\u09b0 (\u098f \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u0985\u09ad\u09bf\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2) \u09aa\u09cd\u09b0\u09ad\u09be\u09ac\u09c7 \u09ac\u09b2\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 \u09a8\u09bf\u099a\u09c7 \u09aa\u09a1\u09bc\u09ac\u09c7 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09aa\u09c3\u09a5\u09bf\u09ac\u09c0 \u0993 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u09b9\u09cd\u09b0\u09be\u09b8 \u09aa\u09be\u09ac\u09c7\u0964 \u098f\u09b0 \u09ab\u09b2\u09c7 \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2 \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf\u09b0 \u0989\u09aa\u09b0 \u09a7\u09a8\u09be\u09a4\u09cd\u09ae\u0995 \u0995\u09be\u099c \u0995\u09b0\u09ac\u09c7\u0964<\/span><\/p>\n

\u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09c3\u09a4 \u098b\u09a3\u09be\u09a4\u09cd\u09ae\u0995 \u0995\u09be\u099c(Negative Work Done by Gravitational Force)<\/b><\/h2>\n

\u09af\u09a6\u09bf r_{b}>r_{a}<\/span><\/span> \u09b9\u09af\u09bc, \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09af\u09a6\u09bf \u0995\u09a3\u09be \u09a6\u09c1\u099f\u09bf\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf \u09aa\u09be\u09af\u09bc, \u09a4\u09be\u09b9\u09b2\u09c7 \\frac{1}{r_{b}}<<\/span>\\frac{1}{r_{a}}<\/span><\/span> \u09b9\u09af\u09bc, \u09ab\u09b2\u09c7 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7 W_{a b}<\/span><\/span>\u00a0\u098b\u09a3\u09be\u09a4\u09cd\u09ae\u0995 \u09b9\u09af\u09bc, \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2 \u098b\u09a3\u09be\u09a4\u09cd\u09ae\u0995 \u0995\u09be\u099c \u09b8\u09ae\u09cd\u09aa\u09a8\u09cd\u09a8 \u0995\u09b0\u09c7\u0964 \u0995\u09a3\u09be\u09a6\u09cd\u09ac\u09af\u09bc\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf \u0995\u09b0\u09a4\u09c7 \u09b9\u09b2\u09c7 \u09ac\u09be\u0987\u09b0\u09c7 \u09a5\u09c7\u0995\u09c7 \u09ac\u09b2 \u09aa\u09cd\u09b0\u09df\u09cb\u0997 \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7, \u09b8\u09c7\u0987 \u09ac\u09be\u09b9\u09cd\u09af\u09bf\u0995 \u09aa\u09cd\u09b0\u09af\u09c1\u0995\u09cd\u09a4 \u09ac\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09c3\u09a4 \u0995\u09be\u099c \u0985\u09ac\u09b6\u09cd\u09af \u09a7\u09a8\u09be\u09a4\u09cd\u09ae\u0995 \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n

\u09af\u09a6\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf\u0995\u09c7 \u0989\u09aa\u09b0\u09c7 \u0993\u09a0\u09be\u09a4\u09c7 \u09af\u09be\u0987 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09aa\u09c3\u09a5\u09bf\u09ac\u09c0 \u0993 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf \u0995\u09b0\u09a4\u09c7 \u09af\u09be\u0987, \u09a4\u09be\u09b9\u09b2\u09c7 \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2\u09c7\u09b0 \u09ac\u09bf\u09b0\u09c1\u09a6\u09cd\u09a7\u09c7 \u0995\u09be\u099c \u0995\u09b0\u09a4\u09c7 \u09b9\u09ac\u09c7 \u09ab\u09b2\u09c7 \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u0995\u09be\u099c \u098b\u09a3\u09be\u09a4\u09cd\u09ae\u0995 \u09b9\u09ac\u09c7, \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u0986\u09ae\u09be\u09a6\u09c7\u09b0 \u09aa\u09cd\u09b0\u09af\u09c1\u0995\u09cd\u09a4 \u09ac\u09b2\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u09a7\u09a8\u09be\u09a4\u09cd\u09ae\u0995 \u0995\u09be\u099c \u09b9\u09ac\u09c7\u0964<\/span><\/p>\n

\u09ac\u09be\u09b9\u09cd\u09af\u09bf\u0995 \u09ac\u09b2 \u09aa\u09cd\u09b0\u09df\u09cb\u0997\u09c7 \u09ac\u09bf\u0995\u09c3\u09a4 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0989\u09aa\u09b0 \u0995\u09be\u099c(Work Done on a Deformed object by External Force)<\/b><\/h2>\n

\u098f\u0996\u09a8 \u0986\u09ae\u09b0\u09be \u098f\u0995\u099f\u09bf \u09a4\u09be\u09b0 \u09ac\u09be \u09a6\u09a8\u09cd\u09a1\u0995\u09c7 \u09aa\u09cd\u09b0\u09b8\u09be\u09b0\u09bf\u09a4 \u0995\u09b0\u09a4\u09c7 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u0985\u09a8\u09c1\u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09ac\u09bf\u0995\u09c3\u09a4\u09bf\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u0995\u09be\u099c \u09b8\u09ae\u09cd\u09aa\u09b0\u09cd\u0995\u09c7 \u0986\u09b2\u09cb\u099a\u09a8\u09be \u0995\u09b0\u09ac\u0964 \u098f\u0995\u099f\u09bf \u09a4\u09be\u09b0\u09c7\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09ac\u09b0\u09be\u09ac\u09b0 \u09ac\u09be\u09b9\u09cd\u09af\u09bf\u0995 \u09aa\u09cd\u09b0\u09b8\u09be\u09b0\u09be\u0999\u09cd\u0995 \u09ac\u09b2 \u0995\u09cd\u09b0\u09bf\u09df\u09be \u0995\u09b0\u09b2\u09c7 \u09a4\u09be\u09b0\u099f\u09bf\u09a4\u09c7 \u0985\u09a8\u09c1\u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09aa\u09c0\u09dc\u09a8 \u09aa\u09cd\u09b0\u09af\u09c1\u0995\u09cd\u09a4 \u09b9\u09df, \u09ab\u09b2\u09c7 \u09b8\u09c7\u099f\u09bf \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af\u09c7 \u09ac\u09be\u09dc\u09c7\u0964 \u0985\u09a4\u098f\u09ac \u09aa\u09cd\u09b0\u09af\u09c1\u0995\u09cd\u09a4 \u09ac\u09b2\u09c7\u09b0 \u09aa\u09cd\u09b0\u09df\u09cb\u0997 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09b0 \u0995\u09bf\u099b\u09c1\u099f\u09be \u09b8\u09b0\u09a3 \u09b9\u09df \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u0995\u09be\u099c \u0995\u09b0\u09be \u09b9\u09df\u0964 \u09b8\u09cd\u09a5\u09bf\u09a4\u09bf\u09b8\u09cd\u09a5\u09be\u09aa\u0995 \u09b8\u09c0\u09ae\u09be\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u0995\u09be\u099c \u09ac\u09bf\u0995\u09c3\u09a4 \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf\u09a4\u09c7 \u09b8\u09cd\u09a5\u09bf\u09a4\u09bf\u09b8\u09cd\u09a5\u09be\u09aa\u0995 \u09b6\u0995\u09cd\u09a4\u09bf\u09b0\u09c2\u09aa\u09c7 \u09ac\u09be \u09b8\u09cd\u09a5\u09bf\u09a4\u09bf\u09b8\u09cd\u09a5\u09be\u09aa\u0995\u09b0\u09c2\u09aa\u09c7 \u09b8\u099e\u09cd\u099a\u09bf\u09a4 \u09b9\u09df\u0964 \u0995\u09cb\u09a8\u09cb \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09c7 \u09a7\u09c0\u09b0\u09c7 \u09a7\u09c0\u09b0\u09c7 \u09aa\u09cd\u09b0\u09b8\u09be\u09b0\u09bf\u09a4 \u0995\u09b0\u09b2\u09c7 \u09aa\u09cd\u09b0\u09af\u09c1\u0995\u09cd\u09a4 \u09ac\u09b2 <\/span>F<\/span> \u0995\u09b0\u09cd\u09a4\u09c3\u0995 \u0995\u09c3\u09a4 \u0995\u09be\u099c \u09ac\u09be \u09b8\u09cd\u09a5\u09bf\u09a4\u09bf\u09b8\u09cd\u09a5\u09be\u09aa\u0995 \u09ac\u09b2 <\/a>\u00a0F_{C}<\/span><\/span>\u00a0\u0995\u09b0\u09cd\u09a4\u09c3\u0995 \u09a7\u09a8\u09be\u09a4\u09cd\u09ae\u0995 \u0995\u09be\u099c \u09a6\u09bf\u09df\u09c7 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09b8\u09cd\u09a5\u09bf\u09a4\u09bf\u09b8\u09cd\u09a5\u09be\u09aa\u0995 \u09b6\u0995\u09cd\u09a4\u09bf\u09b0 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8 \u09aa\u09b0\u09bf\u09ae\u09be\u09aa \u0995\u09b0\u09be \u09af\u09be\u09df\u0964 \u09a8\u09bf\u0989\u099f\u09a8\u09c7\u09b0 \u09a4\u09c3\u09a4\u09c0\u09df \u09b8\u09c2\u09a4\u09cd\u09b0 \u0985\u09a8\u09c1\u09af\u09be\u09df\u09c0 <\/span>F_{C}<\/span><\/span> \u09aa\u09cd\u09b0\u09af\u09c1\u0995\u09cd\u09a4 \u09ac\u09b2 <\/span>F<\/span>-\u098f\u09b0 \u09b8\u09ae\u09be\u09a8 \u0993 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4\u0964<\/span><\/p>\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, \u09b8\u09c1\u09b7\u09ae \u09aa\u09cd\u09b0\u09b8\u09cd\u09a5\u099a\u09cd\u099b\u09c7\u09a6\u09c7\u09b0 \u098f\u0995\u099f\u09bf \u09a4\u09be\u09b0\u09c7\u09b0 \u09aa\u09cd\u09b0\u09be\u09a5\u09ae\u09bf\u0995 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af <\/span>L<\/span> \u098f\u09ac\u0982 \u09aa\u09cd\u09b0\u09b8\u09cd\u09a5\u099a\u09cd\u099b\u09c7\u09a6\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2 <\/span>A<\/span>\u0964 \u09aa\u09cd\u09b0\u09b8\u09be\u09b0\u0995 \u09ac\u09b2 <\/span>F<\/span> \u098f\u09b0 \u0995\u09cd\u09b0\u09bf\u09df\u09be\u09df \u09a4\u09be\u09b0\u099f\u09bf\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf \u09b9\u09b2\u09cb<\/span>\u0964 \u0985\u09a4\u098f\u09ac<\/span><\/p>\n

\u0985\u09a8\u09c1\u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09ac\u09bf\u0995\u09c3\u09a4\u09bf <\/span>==\\frac{l}{L}<\/span><\/span>, \u0985\u09a8\u09c1\u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09aa\u09c0\u09dc\u09a8 <\/span>=<\/span>=\\frac{F}{A}<\/span><\/span><\/p>\n

\u2234<\/span>\u0987\u09df\u0982-\u098f\u09b0 \u0997\u09c1\u09a3\u09be\u0999\u09cd\u0995, Y=\\frac{F \/ A}{l \/ L}=\\frac{F L}{A l}<\/span><\/span><\/p>\n

\u0985\u09a4\u098f\u09ac, <\/span>F=\\frac{\\text { YAl }}{\\text { L }}<\/span><\/span><\/p>\n

\u2234\\therefore F_{c}=\\frac{Y A l}{L}<\/span><\/span><\/p>\n

\u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09a4\u09be\u09b0\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 Y A<\/span><\/span>\u00a0\u098f\u09ac\u0982 <\/span>L<\/span> \u09a7\u09cd\u09b0\u09c1\u09ac\u0995\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \\mathrm{F}_{c} \\propto l<\/span><\/span> , \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09b8\u09cd\u09a5\u09bf\u09a4\u09bf\u09b8\u09cd\u09a5\u09be\u09aa\u0995 \u09ac\u09b2 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf\u09b0 \u09b8\u09ae\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995\u0964 \u09a6\u09c8\u09b0\u09cd\u0998 \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf \u09af\u0996\u09a8 \u09b6\u09c2\u09a8\u09cd\u09af \u09a5\u09c7\u0995\u09c7 \u09ac\u09c7\u09dc\u09c7 l<\/span><\/span> \u09b9\u09df, \\mathrm{F}_{c}<\/span><\/span> \u09a4\u0996\u09a8 \u09b6\u09c2\u09a8\u09cd\u09af \u09a5\u09c7\u0995\u09c7 \u09b0\u09c8\u0996\u09bf\u0995\u09ad\u09be\u09ac\u09c7 \u09ac\u09c7\u09dc\u09c7, \\frac{\\mathrm{YAl}}{\\mathrm{L}}<\/span><\/span>\u00a0\u09b9\u09df\u0964<\/span><\/p>\n

\u0985\u09a4\u098f\u09ac \u09a4\u09be\u09b0\u099f\u09bf\u09b0 <\/span>l<\/span><\/span> \u09aa\u09b0\u09bf\u09ae\u09be\u09a3 \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf\u09b0 \u09b8\u09ae\u09df \u09b8\u09cd\u09a5\u09bf\u09a4\u09bf\u09b8\u09cd\u09a5\u09be\u09aa\u0995 \u09ac\u09b2\u09c7\u09b0 \u0997\u09dc \u09ae\u09be\u09a8, \\frac{Y A l}{2 L}<\/span><\/span> \u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09aa\u09cd\u09b0\u09df\u09cb\u0997 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09b0l<\/span><\/span>\u09aa\u09b0\u09bf\u09ae\u09be\u09a3 \u09b8\u09b0\u09a3\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u098f\u0987 \u09ac\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09be\u099c <\/span>=-\\frac{Y A I}{2 L} \\times l<\/span><\/span><\/p>\n

\u0985\u09a4\u098f\u09ac \u09aa\u09cd\u09b0\u09b8\u09be\u09b0\u09bf\u09a4 \u09a4\u09be\u09b0\u09c7\u09b0 \u09b8\u09cd\u09a5\u09bf\u09a4\u09bf\u09b8\u09cd\u09a5\u09be\u09aa\u0995 \u09ac\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09be\u099c \u09ac\u09be<\/span><\/p>\n

\u09b8\u09cd\u09a5\u09bf\u09a4\u09bf\u09b8\u09cd\u09a5\u09be\u09aa\u0995 \u09b8\u09cd\u09a5\u09bf\u09a4\u09bf\u09b6\u0995\u09cd\u09a4\u09bf <\/span><\/p>\n

\\begin{aligned}\n\n&=-\\left(-\\frac{Y A l^{2}}{2 L}\\right)=\\frac{Y A \/^{2}}{2 L} \\\\\n\n&=\\frac{1}{2}\\left(\\frac{Y A l}{L}\\right) \\times l=\\frac{1}{2} F \\times l\n\n\\end{aligned}<\/span><\/span><\/p>\n

=\\frac{1}{2} \\times<\/span><\/span>\u09aa\u09cd\u09b0\u09af\u09c1\u0995\u09cd\u09a4<\/span>\u00a0<\/span>\u09ac\u09b2<\/span>\u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af<\/span>\u00a0<\/span>\u09ac\u09c3\u09a6\u09cd\u09a7\u09bf<\/span><\/p>\n

\u2234<\/span>\u09b8\u09cd\u09a5\u09bf\u09a4\u09bf\u09b8\u09cd\u09a5\u09be\u09aa\u0995<\/span>\u00a0<\/span>\u09ac\u09b2<\/span>\u00a0<\/span>\u09a6\u09cd\u09ac\u09be\u09b0\u09be<\/span>\u00a0<\/span>\u0995\u09be\u099c<\/span>=\\frac{1}{2} \\times<\/span><\/span>\u09b8\u09cd\u09a5\u09bf\u09a4\u09bf\u09b8\u09cd\u09a5\u09be\u09aa\u0995<\/span>\u00a0<\/span>\u09ac\u09b2<\/span>\u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af<\/span>\u00a0<\/span>\u09ac\u09c3\u09a6\u09cd\u09a7\u09bf<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

\u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2 \u00a0\u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09c3\u09a4 \u0995\u09be\u099c(Work Done by Gravitational Force) \u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf, \u098f \u09ae\u09b9\u09be\u09ac\u09bf\u09b6\u09cd\u09ac\u09c7\u09b0 \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u09a6\u09c1\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09a3\u09be \u098f\u0995\u09c7 \u0985\u09aa\u09b0\u0995\u09c7 \u098f\u0995\u099f\u09bf \u09ac\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u0995\u09b0\u09c7\u0964 \u098f \u09ac\u09b2\u0995\u09c7 \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2 \u09ac\u09b2\u09be \u09b9\u09af\u09bc\u0964 \u098f\u099f\u09bf \u098f\u0995\u099f\u09bf \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8\u09b6\u09c0\u09b2 \u09ac\u09b2\u2014\u09a6\u09c1\u099f\u09bf \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u099c\u09a8\u09cd\u09af \u098f \u09ac\u09b2\u09c7\u09b0 \u09ae\u09be\u09a8 \u09a4\u09be\u09a6\u09c7\u09b0<\/p>\n

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