Question

A particle moving with kinetic energy $=3J$ makes an elastic head-on collision with a stationary particle which has twice its mass. During the impact:

• A. the minimum kinetic energy of the system is $1J$
• B. the maximum elastic potential energy of the system is $2J$
• C. momentum and total energy are conserved at every instant
• D. the ratio of kinetic energy to potential energy of the system first decreases and then increases

Answer 1

The correct option is B the maximum elastic potential energy of the system is $2J$

For minimum Kinetic energy both should have same velocities.

$\frac{1}{2}m{v}^2=3J$

By momentum conservation,

$mv=3mu$

$u=\frac{v}{3}$

Kinetic energy min=$\frac{1}{2}\left(3m\right)\left(\frac{v}{3}{)}^2\right)$

$=\frac{1}{3}\left(\frac{1}{2}m{v}^2\right)=\frac{3}{3}=1J$

So maximum potential energy stored=$3-1=2J$