First slide

Coefficient of restitution

Question

Two spheres A and B of masses m₁ and m₂respectively collide. A is at rest initially and B is moving with velocity v along X-axis. After collision, B has a velocity v/2 in a direction perpendicular to the original direction. The mass A moves after collision in the direction

Moderate

A

same as that of B
B

opposite to that of B
C

$θ = \tan^{- 1} (\frac{1}{2})$ to the X-axis
D

$θ = \tan^{- 1} (\frac{- 1}{2})$ to the X-axis

Solution

Initial momentum, $p_{i} = m_{2} v \hat{i} + m_{1} \times 0$
Final momentum, $p_{f} = m_{2} (v / 2) \hat{j} + m_{1} \times v_{1}$
From law of conservation of momentum,
$p_{i} = p_{f}$
$m_{2} v \hat{i} = m_{2} \frac{v}{2} \hat{j} + m_{1} \times v_{1}$
$v_{1} = \frac{m_{2}}{m_{1}} v \hat{i} - \frac{m_{2}}{m_{1}} \frac{v}{2} \hat{j}$
From this equation, we can find, $tanθ = \frac{1}{2}$
$\Rightarrow$ $θ = \tan^{- 1} (\frac{1}{2})$ to the X-axis.

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