Question

A light and a heavy body, having equal momenta, have equal kinetic energies.

• A. True
• B. False

Answer 1

The correct option is B False

Step 1: Relation between kinetic energy and momentum.

As we know:

Kinetic energy$=\frac{1}{2}m{v}^2$

$$\begin{gathered} \Rightarrow K.E.=\frac{1}{2}m{v}^2 \\ \Rightarrow mK.E.=\frac{1}{2}{\left(mv\right)}^2 \\ \therefore p=mv \end{gathered}$$

Where, $P$is the momentum

$$\begin{gathered} \Rightarrow K.E.=\frac{P^2}{2m} \\ \Rightarrow K.E.\propto \frac{1}{m} \end{gathered}$$

Here we can clearly see that the kinetic energy is inversely proportional to the mass of the object..

Hence, less is the mass, greater is the kinetic energy and greater is the mass, less is the kinetic energy.