First slide

Coefficient of restitution

Question

A ball of mass m, moving with a velocity u, along X-axis, strikes another ball of mass 2 m kept at rest. The first ball comes to rest after collision and the other breaks into two equal pieces. One of the pieces starts moving along the y-axis with a speed V. The velocity of the other piece is

Moderate

A

$\large \sqrt {{V^2} - {u^2}}$
B

V – u
C

u + V
D

$\large \sqrt {{u^2} + {V^2}}$

Solution

Conserving momentum, $\large m\vec v_1+m\vec v_2=m\vec u_1$
$\large \Rightarrow \vec v_2=\vec u_1-\vec v_1=u\hat i-v\hat j$
$\large \therefore |\vec v_2|=\sqrt {u^2+v^2}$

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