Two bodies A and B have same kinetic energies. Compare their velocities if mass of A is four times the mass of B.

Considering Body A:

Let mass of body A = m_a = 4m

Let kinetic energy of body A = K

Let velocity of body A = V_a

Considering Body B:

Mass of body B = m_b = m [∵ mass of A is four times the mass of B]

Kinetic energy of body B = K [∵ A and B have same kinetic energies]

Let velocity of body B = V_b

Given, A and B have same kinetic energies,

∴ $\frac{\text{1}}{\text{2}}$ 4mV_a² = $\frac{\text{1}}{\text{2}}$mV_b²

4mV_a² = mV_b²

$$\begin{aligned}\frac{\text{V}_a^2}{\text{V}_b^2} = \frac{\text{1}}{\text{4}} \\[1em] \Rightarrow \frac{\text{V}_a}{\text{V}_b} = \sqrt{\frac{\text{1}}{\text{4}}} \\[1em] \Rightarrow \frac{\text{V}_a}{\text{V}_b} = \frac{1}{2}\end{aligned}$$

Hence, V_a : V_b = 1 : 2 or velocity of body B is two times the velocity of body A.