Question

A body moving with velocity $v$ has momentum and kinetic energy numerically equal. What is the value of $v$

• A. $2m/s$
• B. $\sqrt{2}m/s$
• C. $1m/s$
• D. $0.2m/s$

Answer 1

The correct option is A

$2m/s$

Step 1. Given data

It is given that momentum and kinetic energy numerically equal

Step 2. Velocity of body $v$

Kinetic energy is $K.E=\frac{1}{2}m{v}^2$

Momentum is $P=mv$

where $m$ is the mass of the body and Velocity of a body $v$

Equating momentum and kinetic energy, we get

$$\begin{gathered} mv=\frac{1}{2}m{v}^2 \\ \Rightarrow v=2m/s \end{gathered}$$

The velocity of the body is $v=2m/s$

Hence, option A is correct.