Work Energy And Power Question 310
Question: Body of mass m moving with a velocity $ v $ in the $ +ve $ X direction collides with a body of mass M moving with a velocity V in the $ +ve $ Y direction. The collision is perfectly inelastic. Mark out the correct statement(s) w.r.t. this situation.
Options:
A) The magnitude of momentum of the composite body is $ \sqrt{{{(mv)}^{2}}+{{(MV)}^{2}}} $
B) The composite body moves in a direction making an angle $ \theta ={{\tan }^{-1}}( \frac{MV}{mv} ) $ with $ +ve $ X-axis.
C) The loss of kinetic energy due to collision
D) All of the above
Show Answer
Answer:
Correct Answer: D
Solution:
[d] As no external force is acting momentum of the system remains conserved, i.e., $ {{\vec{P}} _{f}}=mv\hat{i}+mV\hat{j} $
$ |{{\vec{P}} _{f}}|=\sqrt{{{(mv)}^{2}}+{{(MV)}^{2}}} $
$ \Rightarrow $ $ \tan \theta =\frac{MV}{mv} $ Loss in $ KE==\Delta K $
$ =\frac{mv^{2}}{2}+\frac{MV^{2}}{2}-\frac{1}{2}[ \frac{{{(mv)}^{2}}+{{(MV)}^{2}}}{M+m} ] $
$ =\frac{Mm}{2(M+m)}\times (V^{2}+v^{2}) $
