Question

A batsman hits two balls of different masses $0.5kg$ and $1kg$ out of the stadium, the velocity with which these balls travel is the same. What would be the ratio of their kinetic energies?

• A. 1:2
• B. 2:1
• C. 1:4
• D. 4:1

Answer 1

The correct option is A

1:2

Kinetic energy of an object, $KE=\frac{1}{2}m{v}^2$, where $m$ is the mass of the object and $v$ is the velocity of the object.

Let $v$ be the velocity of both the balls.

Kinetic energy of the ball of mass 0.5 kg = $\frac{1}{2}\times 0.5\times v^2=\frac{v^2}{4}$

Kinetic energy of the ball of mass 1 kg = $\frac{1}{2}\times 1\times v^2=\frac{v^2}{2}$

Therefore, the kinetic energy of the ball with mass 0.5 kg is half the kinetic energy of the ball with mass 1 kg i.e. the ratio of kinetic energies of first ball to second ball is $1:2$.