question_answer

A projectile is projected with a linear momentum p making an angle \[\theta \] with the horizontal. The change in momentum of the projectile on return to the ground will be

A) \[2p\,tan\,\theta \]          

B)         \[2p\,sin\,\theta \]       

C)        \[2p\,cos\,\theta \]         

D)        \[~2p\]

Correct Answer: B

Solution :

\[\left| ({{P}_{f}}-{{P}_{i}}) \right|=\]Change in momentum \[=\sqrt{{{P}^{2}}+{{P}^{2}}+2P.P\,cos\,(\pi -2\theta )}\] \[=P\sqrt{2+2(-cos\theta )}\] \[=P\sqrt{2(si{{n}^{2}}\theta )}\] \[=2P\,\sin \theta \]