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Question

Physics Question on work, energy and power

Two identical masses mm moving with velocities u1u_{1} and u2u_{2} collide perfectly inefasticatiy. Find the loss in energy.

A

m(u1−u22)m\left(u_{1}-u_{2}^{2}\right)

B

m4(u1−u2)2\frac{m}{4}\left(u_{1}-u_{2}\right)^{2}

C

m2(u1−u2)2\frac{m}{2}\left(u_{1}-u_{2}\right)^{2}

D

m(u1−u2)3m\left(u_{1}-u_{2}\right)^{3}

Answer

m4(u1−u2)2\frac{m}{4}\left(u_{1}-u_{2}\right)^{2}

Explanation

Solution

Loss in kinetic energy =12m1m2(u1−u2)2(m1+m2)=\frac{1}{2} \frac{m_{1} m_{2}\left(u_{1}-u_{2}\right)^{2}}{\left(m_{1}+m_{2}\right)} =12m⋅m(u1−u2)2(m+m)=\frac{1}{2} \frac{m \cdot m\left(u_{1}-u_{2}\right)^{2}}{(m+m)} =m4(u1−u2)2=\frac{m}{4}\left(u_{1}-u_{2}\right)^{2}