Question

Two object collides, mass $2m$ is moving with velocity $U$ and mass $m$ is initially at rest. After the collision, the objects move away with velocities $u$ and $v$, as shown in above figure
If the collision is elastic, then

• A. $U^2=u^2-\frac{1}{2v^2}$
• B. ${2U}^2=\frac{3}{2}{u}^2+\frac{1}{4v^2}$
• C. $U=u-\frac{1}{2v}$
• D. $U=u+\frac{1}{2v}$
• E. ${(U-u)}^2=\frac{1}{2v^2}$

Answer 1

The correct option is B ${2U}^2=\frac{3}{2}{u}^2+\frac{1}{4v^2}$

For elastic collision, the kinetic energy is conserved.

Kinetic energy conservation along horizontal:

$\frac{1}{2}\left(2m\right)U^2+\frac{1}{2}m{0}^2=\frac{1}{2}\left(2m\right)(u\cos {30}^o{)}^2+\frac{1}{2}m(v\cos {60}^o{)}^2$

or $2m{U}^2=2m{u}^2(\frac{\sqrt{3}}{2}{)}^2+m{v}^2(1/2{)}^2$

or $2U^2=\left(3/2\right)u^2+\left(1/4\right)v^2$