question_answer

A 20 g bullet pierces through plate of mass \[{{m}_{1}}=1\] kg and then comes to rest inside a second plate of mass \[{{m}_{2}}=2.98\]kg. It is found that the two plates, initially at rest, now move with equal velocities. The percentage loss in the initial velocity of bullet when it is between \[{{m}_{1}}\] and \[{{m}_{2}}\] (neglect any loss of material of the bodies, due to action of bullet) will be

A)  20%                                      

B)  25%

C)  30%                                      

D)  45%

Correct Answer: B

Solution :

The situation is shown in figure. Conserve the momentum for the two cases and then solve the equation. First fake 1st sheet and bullet as the system. \[mu=m{{u}_{1}}+{{m}_{1}}v\] Now take 2nd sheet and bullet as the system. \[m{{u}_{1}}=(m+{{m}_{2}})v\] Solving this equation, we get the value of \[\frac{(u-{{u}_{1}})}{u}\times 100%=25%\]