prove that the second law of motion holds good only for point objects

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Solution

$S e c o n d l a w o f m o t i o n s t a t e s t h a t r a t e o f c h a n g e o f m o m e n t u m i s d i r e c t l y p r o p o r t i o n a l t o t h e f o r c e i m p r e s s e d u p o n t h e b o d y . A c c o r d i n g t o t h i s l a w F α \frac{d P}{d t} I N c a s e t h e b o d y i s s y m m i t r i c a l t h e n t h e f o r c e i m p r e s s e d u p o n t h e b o d y i s d i r e c t e d t o a n d p a s \sin g t h r o u g h t h e l i n e t h a t p a s s e s t h r o u g h i t s c e n t r e a n d w h o l e f o r c e i s t o t a l l y a c t i n g i n t h e d i r e c t i o n o f a c t i o n o f f o r c e . T h i s w a y t h e d e f i n i t i o n o f f o r c e i s d i r e c t l y p r o p o r t i o n a l t o t h e m o m e n t u m .$

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