Question

If the kinetic energy of a body is increased two times, its momentum will

• A. Half
• B. Remain unchanged
• C. Be doubled
• D. Increases $\sqrt{2}$ times

Answer 1

The correct option is D

Increases $\sqrt{2}$ times

Step 1: Given data

The kinetic energy of a body is increased two times,

$K^{\text{'}}=2K$

$K$ = kinetic energy

$K^{\text{'}}$= new Kinetic Energy

Step 2: Formula used

Momentum $\left(\rho \right)$ can be written as,
$\rho =mv$

$v$ is the velocity of the body

$m$ is the mass of the body

The kinetic energy in terms of momentum is $K=\frac{1}{2}m{v}^2$

The relation between kinetic energy and momentum $\left(\rho \right)$ is
$K=\frac{{\rho }^2}{2m}$

or $\rho =\sqrt{2mK}$

Step 3: Evaluate the new momentum

${\rho }^{\text{'}}=\sqrt{2m{K}^{\text{'}}}$

$\rho \text{'}=\sqrt{2m\left(2K\right)}$

$\rho \text{'}=\sqrt{2}\rho$

$\rho$ is the momentum of the body, and $\rho \text{'}$ is the new momentum when kinetic energy is doubled.

So If the kinetic energy of a body is increased two times, its momentum will be $\sqrt{2}$ times the momentum.

Hence, option D is the correct answer.