Question

A particle of mass m moving in the x-direction with speed 2v is hit by another particle of mass 2m moving in the y-direction with speed v. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to

• A. 50%
• B. 56%
• C. 62%
• D. 44%

Answer 1

The correct option is B

56%

Initial energy, $E_1=\frac{1}{2}m(2v{)}^2+\frac{1}{2}(2m)v^2=3m{v}^2$
Now, by momentum conservation, $3mV=2\sqrt{2}mv\Rightarrow V=\frac{2\sqrt{2}v}{3}$
Final energy, $E_2=\frac{1}{2}\left(3m\right)V^2=\frac{4}{3}m{v}^2$
Now, $\frac{E_1-E_2}{E_1}\times 100=56$%