Question

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

• A. the minimum kinetic energy of the system is 1 J
• B. the maximum elastic potential energy of the system is 2J
• C. momentum and total energy are conserved at every instant
• D. All of the above are correct

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A the minimum kinetic energy of the system is 1 J
B the maximum elastic potential energy of the system is 2J
C momentum and total energy are conserved at every instant
D All of the above are correct

In a headon elastic collision between two particles, the kinetic energy becomes minimum andthe potential energy becomes maximum at the instant when the two move with a common velocity.

The momentum and the total energy are conserved at every instant.

Let m and u be the mass and initial velocity respectively of the first particle, 2m, be the mass of the second particle, and v be the common velocity.

Then, $\frac{1}{2}m{u}^2=3J;mu=(m+2m)vorv=\frac{u}{3}$

$\therefore$ The minimum KE of the system =$\frac{1}{3}\left(3m\right){\left(\frac{u}{3}\right)}^2=\left(\frac{1}{2}m{u}^2\right)\frac{1}{3}=1J$

$\therefore$ The maximum PE of the system = 2J