A ball moving with velocity $2m/s$, collides head-on with another stationary ball of double the mass. If the coefficient of restitution is $0.5$, then their velocities (in $m/s)$ after collision will be:

The correct option is B $0,1$

Hint: “Conservation of momentum”

Formula used:

$P_i=P_f$

$e=\frac{\text{velocity of seperation}}{\text{velocity of approach}}$

Solution:

Conservation of momentum,

$m\times 2+2m\times 0=m{v}_1+2m{v}_2$

$v_1+2v_2=2\dots \dots \left(i\right)$

$v_1-v_2=-e(u_1-u_2)$

$-e(2-0)=-\frac{1}{2}\left(2\right)=-1\dots \dots \left(ii\right)$

Solving $v_1=0$,

$v_2=1m/s$

Final Answer: (b).