Q.24. State and prove the law of conservation of linear momentum. Write its two applications. The linear momentum of a lady can change in the direction of applied force. Comment.

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Solution

$A c o r d i n g t o l a w o f c o n s e r v a t i o n o f m o m e n t u m I f n e t e x t e r n a l f o r c e o n a s y s t e m i s z e r o t h e n l i n e a r m o m e n t u m o f s y s t e m w i l l b e c o n s e r v e d W e k n o w \vec{F_{e x t}} = \frac{d \vec{p}}{d t} I f \vec{F_{e x t}} = 0 t h e n \frac{d \vec{p}}{d t} = 0 T h i s m e a n s t h a t \vec{p} = co n s \tan t A p p l i c a t i o n s (1) R e c o i l o f g u n : T h e g u n a n d t h e b u l l e t c o n s t i t u e n t a \sin g l e s y s t e m . B e f o r e t h e g u n i s f i r e d, b o t h t h e g u n a n d t h e b u l l e t i s a t r e s t . T h e r e f o r e, t h e i r t o t a l m o m e n t u m i s z e r o . W h e n t h e g u n i s f i r e d, t h e b u l l e t m o v e s f o r w a r d a n d t h e g u n r e c o i l s b a c k w a r d . (2) R o c k e t p r o p u l s i o n : W h e n t h e f u e l o f r o c k e t i s e x p l o d e d, g a s e s e s c a p e w i t h a l a r g e v e l o c i t y a n d h e n c e a l a r g e m o m e n t u m . T h e e s c a p i n g g a s e s, i n t u r n, i m p a r t a n e q u a l a n d o p p o s i t e m o m e n t u m t o t h e r o c k e t . Y e s t h e l i n e a r m o m e n t u m o f a b o d y c h a n g e s i n t h e d i r e c t i o n o f a p p l i e d f o r c e . \frac{d \vec{p}}{d t} = \vec{F_{e x t}} d \vec{p} = \vec{F_{e x t}} d t d \vec{p} i s s m a l l c h a n g e i n l i n e a r m o m e m n t u m \vec{p}, w h i c h i s e q u a l t o \vec{F_{e x t}} d t T h e r e f o r e d \vec{p} i s i n t h e d i r e c t i o n o f \vec{F_{e x t}} H e n c e l i n e a r m o m e n t u m o f a b o d y c h a n g e s i n t h e d i r e c t i o n o f a p p l i e d f o r c e .$

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