{"id":2524,"date":"2022-03-24T11:21:35","date_gmt":"2022-03-24T11:21:35","guid":{"rendered":"https:\/\/stage-wp.10minuteschool.com\/?p=2524"},"modified":"2022-03-24T05:42:51","modified_gmt":"2022-03-24T05:42:51","slug":"gravitational-force-work","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/gravitational-force-work\/","title":{"rendered":"\u0985\u09ad\u09bf\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2 \u0993 \u0995\u09be\u099c"},"content":{"rendered":"

\u0985\u09ad\u09bf\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2\u09c7\u09b0 <\/b>\\left(F \\propto \\frac{1}{r^{2}}\\right)<\/span><\/span> \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4\u09c7 \u0995\u09be\u099c (Work Done Against 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\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\u0987 \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 \\text {(F)}<\/span><\/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 F \\propto \\frac{1}{r^{2}} I<\/span><\/span>\u0964 <\/span>\u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf, <\/span>m<\/span> \u098f\u09ac\u0982 <\/span>M<\/span> \u09ad\u09b0\u09c7\u09b0 \u09a6\u09c1\u099f\u09bf \u0995\u09a3\u09be \u09aa\u09b0\u09b8\u09cd\u09aa\u09b0 \u09a5\u09c7\u0995\u09c7 \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 \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u09ac\u09b2,<\/span><\/p>\nF=\\frac{G M m}{r^{2}}<\/span>\n

\u09a6\u09c1\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u098f\u0995\u099f\u09bf \u09af\u09a6\u09bf \u09b9\u09df \u09aa\u09c3\u09a5\u09bf\u09ac\u09c0 \u09a4\u09be\u09a4\u09c7 \u09af\u09c7 \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u09b9\u09df \u09a4\u09be\u0995\u09c7 \u0985\u09ad\u09bf\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2 (Gravitational force)<\/strong> \u09ac\u09b2\u09c7 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u0995\u09cb\u09a8\u09cb \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0989\u09aa\u09b0 \u09aa\u09c3\u09a5\u09bf\u09ac\u09c0\u09b0 \u0986\u0995\u09b0\u09cd\u09b7\u09a3\u0995\u09c7 \u0985\u09ad\u09bf\u0995\u09b0\u09cd\u09b7 (gravitational force) \u09ac\u09b2\u09c7\u0964 \u09a7\u09b0\u09be \u09af\u09be\u0995, M =<\/span>\u00a0<\/span>\u09aa\u09c3\u09a5\u09bf\u09ac\u09c0\u09b0 \u09ad\u09b0, \\text {R}<\/span><\/span>\u00a0=<\/span> \u09aa\u09c3\u09a5\u09bf\u09ac\u09c0\u09b0 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7, <\/span>m=\\bar{\\varepsilon}-<\/span><\/span> \u09ad\u09c2-\u09aa\u09c3\u09b7\u09cd\u09a0\u09c7 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4 \u0995\u09cb\u09a8\u09cb \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09ad\u09b0 <\/span>\\text {r}<\/span>=<\/span> \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0993 \u09aa\u09c3\u09a5\u09bf\u09ac\u09c0\u09b0 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09b0\u09cd\u09a4\u09c0 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac\u0964 \u09a4\u09be\u09b9\u09b2\u09c7 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0989\u09aa\u09b0 \u0985\u09ad\u09bf\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2,<\/span><\/p>\nF_{G}=-\\frac{G M m}{r^{2}}<\/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 \u09aa\u09c3\u09a5\u09bf\u09ac\u09c0 \u098f\u0987 \u09ac\u09b2\u09c7 \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf\u0995\u09c7 \u09a4\u09be\u09b0 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 \u0986\u0995\u09b0\u09cd\u09b7\u09a3 \u0995\u09b0\u09c7\u0964 \u098f\u0996\u09a8 \u09af\u09a6\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf\u0995\u09c7 \u09ad\u09c2-\u09aa\u09c3\u09b7\u09cd\u09a0 \u09a5\u09c7\u0995\u09c7 <\/span>\\text {h}<\/span><\/span> \u0989\u099a\u09cd\u099a\u09a4\u09be\u09df \u0993\u09a0\u09be\u09a4\u09c7 \u09b9\u09df \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf r = R<\/span> \u09a5\u09c7\u0995\u09c7 <\/span>r=R+h<\/span>\u00a0\u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8\u09c7 \u09af\u09be\u09df \u09a4\u0996\u09a8 \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf\u09b0 \u0989\u09aa\u09b0 \u09aa\u09c3\u09a5\u09bf\u09ac\u09c0 F_{G}=-\\frac{G M m}{r^{2}}<\/span><\/span>\u00a0\u09ac\u09b2 \u09aa\u09cd\u09b0\u09df\u09cb\u0997 \u0995\u09b0\u09c7<\/span>\u0964 <\/span>\u098f \u09ac\u09b2\u09c7\u09b0 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4\u09c7 \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf\u0995\u09c7 <\/span>h<\/span> \u0989\u099a\u09cd\u099a\u09a4\u09be\u09df \u0993\u09a0\u09be\u09a4\u09c7 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf\u09b0 <\/span>h<\/span> \u09b8\u09b0\u09a3 \u0998\u099f\u09be\u09a8\u09cb\u09b0 \u099c\u09a8\u09cd\u09af \u09ac\u09be\u0987\u09b0\u09c7 \u09a5\u09c7\u0995\u09c7 \u0985\u09ad\u09bf\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8 \u0993 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4 F=-F_{G}=\\frac{G M m}{r^{2}}<\/span><\/span>\u00a0\u09ac\u09b2 \u09aa\u09cd\u09b0\u09df\u09cb\u0997 \u0995\u09b0\u09a4\u09c7 \u09b9\u09df<\/span>\u0964 <\/span>\u098f \u09ac\u09b2\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u0995\u09c3\u09a4 \u0995\u09be\u099c,<\/span><\/p>\nW=\\int_{r=R}^{r=R+h}\\\\<\/span>\n=\\int_{R}^{R+h} \\frac{G M m}{r^{2}} d r\\\\<\/span>\n=G M m \\int_{R}^{R+h} \\frac{d r}{r^{2}}\\\\<\/span>\n=G M m\\left[-\\frac{1}{r}\\right]_{R}^{R+h}\\\\<\/span>\n=G M m\\left(-\\frac{1}{R+h}+\\frac{1}{R}\\right)\\\\<\/span>\n\\therefore W=G M m\\left(\\frac{1}{R}-\\frac{1}{R+h}\\right)\\\\<\/span>\n\\begin{array}{l}\n\n\\text { \u09ac\u09be, } W=G M m \\frac{R+h-R}{R(R+h)} \\\\\n\n\\therefore W=\\frac{G M m h}{R(R+h)}\n\n\\end{array}<\/span>\n

\u098f\u0996\u09a8 \u09aa\u09c3\u09a5\u09bf\u09ac\u09c0\u09b0 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 <\/span>R<\/span> \u098f\u09b0 \u09a4\u09c1\u09b2\u09a8\u09be\u09df \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09b8\u09b0\u09a3 <\/span>h<\/span> \u0996\u09c1\u09ac \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u09b9\u09df \u0985\u09b0\u09cd\u09a5\u09be\u09ce <\/span>h<<R<\/span> <\/span>\u09b9\u09df, \u09a4\u09be\u09b9\u09b2\u09c7 \u098f\u0987 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7 <\/span>R<\/span> \u098f\u09b0 \u09a4\u09c1\u09b2\u09a8\u09be\u09df \u09b9\u09b0\u09c7\u09b0 <\/span>h<\/span> \u0995\u09c7 \u0989\u09aa\u09c7\u0995\u09cd\u09b7\u09be \u0995\u09b0\u09c7 \u0986\u09ae\u09b0\u09be \u09aa\u09be\u0987,<\/span><\/p>\nW=\\frac{G M m}{R^{2}} h<\/span>\n

\u0986\u09ac\u09be\u09b0, \u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf, g=\\frac{G M}{R^{2}}<\/span><\/span><\/p>\n

\\therefore w=m g h<\/span><\/span><\/p>\n

\u0985\u09ad\u09bf\u0995\u09b0\u09cd\u09b7\u09c0\u09df \u09ac\u09b2 \u0995\u09b0\u09cd\u09a4\u09c3\u0995 \u0995\u09be\u099c\u09c7\u09b0 \u0989\u09a6\u09be\u09b9\u09b0\u09a3(W<\/b>ork<\/b> D<\/b>one<\/b> B<\/b>y<\/b> G<\/b>ravitational <\/b>F<\/b>orce<\/b>)<\/b><\/h2>\n

(\u0995) \u09ac\u09b8\u09cd\u09a4\u09c1 \u09a8\u09bf\u099a\u09c7 \u09aa\u09a4\u09a8\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u0995\u09be\u099c :<\/b><\/h3>\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, <\/span>\u2018m\u2019<\/span> \u09ad\u09b0\u09ac\u09bf\u09b6\u09bf\u09b7\u09cd\u099f \u098f\u0995\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09c7 \u0985\u09ad\u09bf\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2\u09c7\u09b0 \u09aa\u09cd\u09b0\u09ad\u09be\u09ac\u09c7 <\/span>\u2018h\u2019<\/span> \u0989\u099a\u09cd\u099a\u09a4\u09be \u09b9\u09a4\u09c7 \u09ab\u09c7\u09b2\u09be \u09b9\u09b2\u09cb\u0964<\/span><\/p>\n

\\therefore<\/span> \u0995\u09c3\u09a4 \u0995\u09be\u099c = \u09ac\u09b2 \\times<\/span> \u09b8\u09b0\u09a3<\/p>\n

\u09ac\u09be, W=F \\times h=m g h<\/span>\u00a0 \u00a0[\\because F=m g]<\/span><\/span><\/p>\n

\u09ac\u09be, <\/span>W=<\/span>\u09ad\u09b0 \\times<\/span> <\/span>\u0985\u09ad\u09bf\u0995\u09b0\u09cd\u09b7\u099c<\/span>\u00a0<\/span>\u09a4\u09cd\u09ac\u09b0\u09a3 \\times<\/span> <\/span>\u0989\u099a\u09cd\u099a\u09a4\u09be<\/span><\/p>\n

\u0995\u09be\u099c\u0995\u09c7 \u0985\u09ad\u09bf\u0995\u09b0\u09cd\u09b7\u09c0\u09df \u098f\u0995\u0995\u09c7 \u09aa\u09cd\u09b0\u0995\u09be\u09b6 \u0995\u09b0\u09b2\u09c7, <\/b>W=m g h<\/span><\/span>\u00a0<\/b><\/p>\n

(\u0996) \u09ac\u09b8\u09cd\u09a4\u09c1 \u0989\u09aa\u09b0\u09c7 \u0989\u09a0\u09be\u09a8\u09cb\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u0995\u09be\u099c :<\/b><\/h3>\n

\u2018m\u2019<\/span> \u09ad\u09b0\u09ac\u09bf\u09b6\u09bf\u09b7\u09cd\u099f \u098f\u0995\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09c7 \u0985\u09ad\u09bf\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2\u09c7\u09b0 \u09ac\u09bf\u09b0\u09c1\u09a6\u09cd\u09a7\u09c7 <\/span>\u2018h\u2019<\/span> \u0989\u099a\u09cd\u099a\u09a4\u09be\u09df \u0989\u09aa\u09b0\u09c7 \u0989\u09a0\u09be\u09b2\u09c7<\/span><\/p>\n

\u0995\u09be\u099c <\/span>= <\/span>\u09ad\u09b0 \\times<\/span> <\/span>\u0985\u09ad\u09bf\u0995\u09b0\u09cd\u09b7\u09c0\u09df<\/span>\u00a0<\/span>\u09a4\u09cd\u09ac\u09b0\u09a3 \\times<\/span> <\/span>\u0989\u099a\u09cd\u099a\u09a4\u09be<\/span> \u09ac\u09be, <\/span>W=m g h<\/span><\/span><\/p>\n

\u0985\u09ac\u09b6\u09cd\u09af \u098f \u0995\u09be\u099c<\/a> \u098b\u09a3\u09be\u09a4\u09cd\u09ae\u0995\u0964<\/span><\/p>\n

(\u0997) \u0986\u09a8\u09a4 \u09a4\u09b2 \u09ac\u09c7\u09df\u09c7 \u09a8\u09be\u09ae\u09be\u09a8\u09cb\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u0995\u09be\u099c :<\/b><\/h3>\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, <\/span>\u2018m\u2019<\/span> \u09ad\u09b0\u09ac\u09bf\u09b6\u09bf\u09b7\u09cd\u099f \u098f\u0995\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1 \u0995\u09cb\u09a8\u09cb \u098f\u0995\u099f\u09bf \u09ae\u09b8\u09c3\u09a3 \u09a8\u09ad\u09a4\u09b2 \u09ac\u09c7\u09df\u09c7 <\/span>A<\/span> \u09b9\u09a4\u09c7 <\/span>B<\/span>-\u09a4\u09c7 \u09b8\u09b0\u09c7 \u098f\u09b2\u0964 \u09af\u09a6\u09bf <\/span>g<\/span> \u0985\u09ad\u09bf\u0995\u09b0\u09cd\u09b7\u09c0\u09df \u09a4\u09cd\u09ac\u09b0\u09a3 \u09b9\u09df, \u09a4\u09ac\u09c7 \u0985\u09ad\u09bf\u0995\u09b0\u09cd\u09b7\u09c0\u09df \u09ac\u09b2 \\text {m g}<\/span><\/span>\u00a0\u09ac\u09b8\u09cd\u09a4\u09c1\u099f\u09bf\u0995\u09c7 \u0996\u09be\u09dc\u09be\u09ad\u09be\u09ac\u09c7 \u09a8\u09bf\u099a\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 \u099f\u09be\u09a8\u09ac\u09c7\u0964<\/span><\/p>\n

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

\u09a7\u09b0\u09bf \u09b8\u09b0\u09a3\u09c7\u09b0 \u0985\u09ad\u09bf\u09ae\u09c1\u0996 \u098f\u09ac\u0982 \u0985\u09ad\u09bf\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2\u09c7\u09b0 \u0985\u09ad\u09bf\u09ae\u09c1\u0996\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \\theta<\/span>\u00a0<\/span> \u0995\u09cb\u09a3 \u0986\u099b\u09c7 \u098f\u09ac\u0982 A B=s<\/span><\/span><\/p>\n

\u2234<\/span>\u0985\u09ad\u09bf\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2 <\/span>\\text {m g}<\/span><\/span>-\u098f\u09b0 \u09a6\u09bf\u0995\u09c7 \u09b8\u09b0\u09a3\u09c7\u09b0 \u0985\u0982\u09b6 <\/span>= s \\cos \\theta<\/span><\/span><\/p>\n

\u098f\u0996\u09a8 <\/span>A C=h<\/span><\/span> \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac<\/span><\/p>\n

\\therefore h=s \\cos \\theta<\/span><\/span><\/p>\n

\\therefore<\/span> \u0995\u09be\u099c W= m <\/span> gs \\cos \\theta<\/span> \u09ac\u09be, W=m g h<\/span><\/p>\n

\u09a4\u09b2\u099f\u09bf<\/span>\u00a0<\/span>\u0985\u09a8\u09c1\u09ad\u09c2\u09ae\u09bf\u0995\u09c7\u09b0<\/span>\u00a0<\/span>\u09b8\u09be\u09a5\u09c7<\/span> \\alpha<\/span> <\/span>\u0995\u09cb\u09a3\u09c7<\/span>\u00a0<\/span>\u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8<\/span>\u00a0<\/span>\u0995\u09b0\u09b2\u09c7<\/span>, 0=\\left(90^{\\circ}-\\alpha\\right)<\/span><\/span><\/p>\n

\\therefore W=m <\/span> gs \\cos \\left(90^{\\circ}-\\alpha\\right)=m g s \\sin \\alpha<\/span><\/p>\n

\u09b8\u09cd\u09a5\u09bf\u09a4\u09bf\u09b8\u09cd\u09a5\u09be\u09aa\u0995 \u09ac\u09b2 \u098f\u09ac\u0982 \u0985\u09ad\u09bf\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09be\u099c \u09a5\u09c7\u0995\u09c7 \u09a6\u09c7\u0996\u09be \u09af\u09be\u09df \u09af\u09c7,<\/span><\/p>\n

\u09b8\u09cd\u09a5\u09bf\u09a4\u09bf\u09b8\u09cd\u09a5\u09be\u09aa\u0995 \u09ac\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09be\u099c, W=\\frac{1}{2} \\mathrm{kx}^{2}: \\therefore<\/span><\/span>\u00a0\u0995\u09be\u099c, W \\propto(\\text { \u09b8\u09b0\u09a3 })^{2}<\/span><\/span><\/p>\n

\u0985\u09a8\u09cd\u09af\u09a6\u09bf\u0995\u09c7 \u0985\u09ad\u09bf\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09be\u099c, W=m g h ~ \\therefore<\/span> <\/span>\u0995\u09be\u099c, <\/span>W \\propto<\/span> <\/span>\u09b8\u09b0\u09a3<\/span><\/p>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09ac\u09b2\u09be \u09af\u09be\u09df, \u09b8\u09cd\u09a5\u09bf\u09a4\u09bf\u09b8\u09cd\u09a5\u09be\u09aa\u0995 \u09ac\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09be\u099c \u09b8\u09b0\u09a3\u09c7\u09b0 \u09ac\u09b0\u09cd\u0997\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995\u0964 \u0985\u09aa\u09b0 \u09a6\u09bf\u0995\u09c7 \u0985\u09ad\u09bf\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09be\u099c \u0989\u099a\u09cd\u099a\u09a4\u09be\u09b0 \u09ac\u09be \u09b8\u09b0\u09a3\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995\u0964 \u0985\u09ad\u09bf\u0995\u09b0\u09cd\u09b7 \u09a4\u09cd\u09ac\u09b0\u09a3\u09c7\u09b0 \u09ae\u09be\u09a8 \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf \u09aa\u09c7\u09b2\u09c7 \u098f\u0987 \u09ac\u09b2 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0995\u09be\u099c\u0993 \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf \u09aa\u09be\u09df\u0964<\/span><\/p>\n

(\u0998)\u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u0995\u09be\u099c\u00a0<\/b><\/h3>\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09bf <\/span>M<\/span> \u09ad\u09b0\u09c7\u09b0 \u098f\u0995\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1 \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7\u09b0 <\/span>P<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4\u0964 <\/span>P<\/span> \u09a5\u09c7\u0995\u09c7 <\/span>r\u00a0<\/span>\u09a6\u09c2\u09b0\u09c7 <\/span>m<\/span> \u09ad\u09b0\u09c7\u09b0 \u0985\u09a8\u09cd\u09af \u098f\u0995\u099f\u09bf \u09ac\u09b8\u09cd\u09a4\u09c1 <\/span>Q<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4 [\u099a\u09bf\u09a4\u09cd\u09b0]\u0964 \u098f\u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 <\/span>m<\/span> \u09ad\u09b0\u09c7\u09b0 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0989\u09aa\u09b0 \u0995\u09cd\u09b0\u09bf\u09df\u09be\u09b6\u09c0\u09b2 \u09ae\u09b9\u09be\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2,\u00a0<\/span><\/p>\n

F=\\frac{G M m}{r^{2}}<\/span> \u09a6\u09bf\u0995 \\text {Q P}<\/span><\/span>\u00a0\u09ac\u09b0\u09be\u09ac\u09b0\u0964<\/span><\/p>\n

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

\u098f\u0996\u09a8 <\/span>m<\/span> \u09ad\u09b0\u09c7\u09b0 \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09c7 \u0985\u09b8\u09c0\u09ae \u09b9\u09a4\u09c7 \u0995\u09cd\u09b7\u09c1\u09a6\u09cd\u09b0 \u09a6\u09c1\u09b0\u09a4\u09cd\u09ac <\/span>\\text {d r}<\/span><\/span> \u09b8\u09b0\u09bf\u09df\u09c7 <\/span>R<\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u0986\u09a8\u09a4\u09c7 \u0995\u09c3\u09a4 \u0995\u09be\u099c<\/span><\/p>\n\\begin{aligned}\n\nW &=\\int_{\\infty}^{r} F d r \\cos 0^{\\circ} \\\\\n\n&=\\int_{\\infty}^{r} F d r=\\int_{\\infty}^{r} \\frac{G M m}{r^{2}} d r \\\\\n\n&=G M m \\int_{\\infty}^{r} r^{-2} d r=-G M m\\left[\\frac{1}{r}\\right]_{\\infty}^{r} \\\\\n\n&=-G M m\\left(\\frac{1}{r}-\\frac{1}{\\infty}\\right)=-G M m\n\n\\end{aligned}<\/span>\n

\u09af\u09c7\u09b9\u09c7\u09a4\u09c1 \\frac{G M m}{R^{2}}<\/span><\/span>\u00a0\u098f\u0995\u099f\u09bf \u09a7\u09cd\u09b0\u09c1\u09ac\u0995<\/span><\/p>\n

\\therefore W \\propto h<\/span><\/span><\/p>\n

\u0985\u09b0\u09cd\u09a5\u09be\u09ce \u0985\u09ad\u09bf\u0995\u09b0\u09cd\u09b7\u09c7\u09b0 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4\u09c7 \u0995\u09be\u099c \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09b8\u09b0\u09a3\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995\u0964<\/b><\/p>\n","protected":false},"excerpt":{"rendered":"

\u0985\u09ad\u09bf\u0995\u09b0\u09cd\u09b7 \u09ac\u09b2\u09c7\u09b0 \u09ac\u09bf\u09aa\u09b0\u09c0\u09a4\u09c7 \u0995\u09be\u099c (Work Done Against 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\u0987 \u09ac\u09b2\u09c7\u09b0 \u09ae\u09be\u09a8<\/p>\n

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":[4239,3028,50,51],"tags":[1899,32,1898,1900,1901],"_links":{"self":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/2524"}],"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=2524"}],"version-history":[{"count":10,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/2524\/revisions"}],"predecessor-version":[{"id":12405,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/posts\/2524\/revisions\/12405"}],"wp:attachment":[{"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/media?parent=2524"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/categories?post=2524"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/10minuteschool.com\/content\/wp-json\/wp\/v2\/tags?post=2524"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}