# Π i 1 i 2 ϖ lµ³º ϖ i 1 i 1 i 2 ϖ ø l³æø½

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ϖ 0 = ( I 1 + I 2 ) ϖ lµ³±º . ϖ = I 1 I 1 + I 2 ϖ 0 °Ø´ l³ÆØ½´ Ø²·± oeØL²Ø¶´ ´Ø¸l²°´ .ªÆ±Æ oeØÆ³ÆØæ °Ø´ ´Ø¼ÆÆ oeØL²Ø¶´ ´Ø¸l²°´ (Æ) E i = 1 2 I 1 ϖ 2 0 °Ø´ l³ÆØ½´ Øl½°³ . E f = 1 2 ( I 1 + I 2 ) ϖ 2 = I 1 I 1 + I 2 1 2 I 1 ϖ 2 0 °Ø´ E i - E f ´ªÆ°ø ´Ø¸l²°´ »º± . E i - E f = I 2 I 1 + I 2 1 2 I 1 ϖ 2 0 = I 2 I 1 + I 2 E i (¸) ø ±Æ¶² ¾° I 1 I 2 º° .i ϖ ϖ 0 . E i - E f E i 1 .(oeØoe±½oe´´ ´Ø¸l²°± æ½ØÆ) ½Ø²¾ ´Ø¸l²°´ ªæ·´³ ´²oeøµ °± L¼µº oeØoeØ³³¾´ oe³lØ´µ´ lµ³±º ¾° I 1 = I 2 º° .ii ϖ = 1 2 ϖ 0 . E i - E f E i = 1 2 .oeªÆ³° oeØL²Ø¶´ ´Ø¸l²°´µ Ø¹½ ,lµ³±º ¾° I 1 I 2 º° .iii ϖ I 1 I 2 ϖ 0 ϖ 0 . E i - E f E i I 1 I 2 1 .oeªÆ³° oeØL²Ø¶´ ´Ø¸l²°´ Æ³l³ ( ϖ 0 -± oeØæ½Ø) oel¹³¼ L¼µº oeºl¼µ´ lµ³±º .5 .æ·° °³´ ³±ø ØoeØ³³¾´ ¼²oe´ »º±³ ¼² °± L³µ´ oe³ø¸²oe´´ Ø²·± .L³µ´ ±ø lØ¹´ oeª³¶² ÆØÆæ (¼Ø±¶³ L³µ) oeºl¼µ´ ±ø ØoeØ³³¾´ ¼²oe´ oe° Æø½² (°) ¶½lµ´ ±ø ÆØºl´) ³± oeÆ¹Ø²´ ¼³l¾´ ±³·º ¼Ø±¶´ ±ø ¼²oe´ oe±·ºµ± ´³³ø ³±ø ØoeØ³³¾´ ¼²oe´ .lØ¹± æ½ØÆ ØoeØ³³¾ ¼²oe ºØØ¶ »º ,oe°¾ oeµ³¼± ,¼Ø±¶± oe³ø¸²oe´´ Ø²·± L i ØoeØ³³¾´ ¼²oe± ºl³oe ¼Ø±¶´ ¶lø »³³Øº . a · mv 0 °³´ ¼Ø±¶´ ±ø ¼²oe´ »º± . a ¶½lµ´ °Ø´ ³¾ ¼³l¾ .(oe³lØ´µ± Æ¹Ø² °³´ø lØ¹´µ ¾° . L i = a · mv 0 »º±³ ³µ¹¼ lØ¹Æ ±¼³· ±Ø¼·µ lØ¹´ø ½º´ .´ºØøµ´ ½º³ L³µ´ ±¼ ±Ø¼·µ lØ¹´ø ½º´ º´ oeºl¼µ´ ±¼ ºØªÆ³¼´ ºØªØ½Ø´ oe³½³º´ ,oe³ø¸²oe´´ oe¼Æ °± ´ºØøµ´ ½º º¸ »º± .½º´ ±¼³· ´Æ ´ª³¶²± ª¼³ lØ¹´µ l³L¶³´ ³µº »³³Øº ³oe°Æ ±¼³· ,oe³ø¸²oe´´ oe¼Æ ,´ºØøµ´ ½º ,»º ³µº .L²µ³µ ±Ø¼·µ °± l½°± (L³µ´ ±ø lØ¹´ ÆØÆæ) L f ØoeØ³³¾´ ¼²oe´ »º±³ lµø² ØoeØ³³¾´ ¼²oe´ Ø¾° oeºl¼µ´ ±¼ ºØ±¼³·ø ºØØ²³¹Ø½ ºØL²µ³µ »Ø°ø »³³Øº .L²µ³µ ±Ø¼·µ °³´ oe³ø¸²oe´´ . L f = a · mv 0 6
(¾¾ °± L³µ´) ¼Ø±¶´ ±ø ¼²oe´ L³ø· °³´ oe³ø¸²oe´´ Ø²·± oeºl¼µ´ ±ø p i Ø³³¶´ ¼²oe´ (Æ) . p i = mv 0 øµoeø² (±Ø¼·µ lØ¹´ø ½º´ :ºØØ²³¹Ø½ oe³½³º ºØ±¼³· Øº lµø² ½lº´Æ °±) oe³ø¸²oe´´ l½°± ªØØµ oeºl¼µ´ ±ø Ø³³¶´ ¼²oe´ oe° oe° °³¹µ± Øªº r CM ϖ °Ø´ ´æµ´ ¾ºlµ oe³lØ´µ ¾°³ ,oeºl¼µ´ ±ø ϖ oeØoeØ³³¾´ oe³lØ´µ´ oe° °¹µ² .(oe³ø¸²oe´´ l½°± ªØØµ) oeºl¼µ´ ±ø ØoeØ³³¾´ ¼²oe´ l³µØøÆ . ( m + M ) r CM ϖ ¾° °³´ oeºl¼µ´ ±ø Ø³³¶´ ¼²oe´ .lØ¹´µ (¼Ø±¶´³ L³µ´ ±ø) ´æµ´ ¾ºlµ ¶½lµ °³´ r CM lø°º »³³Øºµ .¼Ø±¶´³ L³µ´ ±ø (lØ¹´ ÆØÆæ) ´Ø¹l²Ø°´ L²µ³µ °³´ I m + M lø°º , L f = I m + M ϖ f ºØØ¶µ oe³ø¸²oe´´ l½°± ªØØµ L f ØoeØ³³¾´ ¼²oe´ ¾° ´Ø¹l²Ø° ØL²µ³µ º³ºæ± lø·°ø . I m + M = ma 2 + 1 3 Ml 2 ( L f = a · mv 0 ) ºØØ¶µ ϖ f -ø »°ºµ . ϖ f = L f I m + M = a · mv 0 ma 2 + 1 3 Ml 2 °³´ ,lØ¹´ oeª³¶²µ ,¼Ø±¶´ æ³±· L³µ´ ±ø r CM ´æµ´ ¾ºlµ r CM = ma + 1 2 Ml m + M

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