Question

A body of mass 'm' moving with a speed 'v' suffers an inelastic collision with another body of 'M' at rest and sticks to it, the ratio of the final kinetic energy of the system to the initial kinetic energy is

• A. $\left(\frac{m}{m+M}\right)$
• B. $\left(\frac{M}{m+M}\right)$
• C. $\left(\frac{m+M}{m}\right)$
• D. $\left(\frac{m+M}{M}\right)$

Answer 1

The correct option is A $\left(\frac{m}{m+M}\right)$

Apply conservation of momentum to find the speed of system after collision
Initial $KE=\frac{1}{2}m{v}^2.FinalKE=\frac{1}{2}(m+M)V^2$. Therefore,
$\frac{FinalKE}{InitialKE}=\left(\frac{m+M}{m}\right)\frac{V^2}{v^2}=\frac{m}{m+M}$
Hence the correct choice is (a).