First slide

Line of impact

Question

On a frictionless surface, a block of mass M moving at speed $ν$ collides elastically with another block of same mass M which is initially at rest. After collision the first block moves at an angle $θ$ to its initial direction and has a speed $\frac{ν}{3}$ . The second block's speed after the collision is

Moderate

A

$\frac{3}{\sqrt{2}} v$
B

$\frac{\sqrt{3}}{2} v$
C

$\frac{2 \sqrt{2}}{3} v$
D

$\frac{3}{4} v$

Solution

The situation is shown in the figure.
Let $ν'$ be speed of second block after the collision. As the collision is elastic, so kinetic energy is conserved. According to conservation of kinetic energy,
$\frac{1}{2} M v^{2} + 0 = \frac{1}{2} M {(\frac{v}{3})}^{2} + \frac{1}{2} M v^{' 2}$
$v^{2} = \frac{v^{2}}{9} + v^{' 2}$
$or v^{' 2} = v^{2} - \frac{v^{2}}{9} = \frac{9 v^{2} - v^{2}}{9} = \frac{8}{9} v^{2}$
$v^{'} = \sqrt{\frac{8}{9} v^{2}} = \frac{\sqrt{8}}{3} v = \frac{2 \sqrt{2}}{3} v$

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