Question

A body of mass $10kg$ is moving with a velocity $20m{s}^{-1}$. If the mass of the body is doubled and its velocity is halved, find the ratio of the initial kinetic energy to the final kinetic energy.

Answer 1

Given , Mass of object, $m=10kg$

Velocity of object, $v=20m{s}^{-1}$

Initial Kinetic energy, $K_1=\frac{1}{2}\times 10\times {20}^2=2000J$

Now, Final mass, $m_2=20kg$

Final Velocity, $v_2=10m/s$

Final Kinetic energy, $K_2=\frac{1}{2}\times 20\times {10}^2=1000J$

Required Ratio = $\frac{K_1}{K_2}=\frac{2000}{1000}=2:1$