Question

A ball moving with velocity $2\, m/s$ 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

• A. 0, 1
• B. 44562
• C. 1, 0.5
• D. 0, 2

Answer 1

The Correct Option is A

Here, m$_1$ = w, m$_2$ = 2m
u$_1$= 2 m/s, u$_2$ = 0
Coefficient of restitution, e = 0.5
Let v$_1$ and v$_2$ be their respective velocities after collision.
Applying the law of conservation of linear momentum, we get
$m_1u_1+m_2u_2=m_1v_1+m_2v_2$
$\therefore m \times 2 +2m \, \, \times \, 0 = m\times v_1 +2m \times v_2$
or $2m = mv_1 + 2mv_2$
or 2 = ($v_1$ + 2$v_2) $ ...(i)
By definition of coefficient of restitution,
$e=\frac{v_2 -v_1}{u_1 -u_2}$
or $e(u_1 -u_2)=v_2-v_1$
0.5(2 - 0) = $v_2 - v_1 $ ...(ii)
$1=v_2-v_1$
Solving equations (i) and (ii), we get
$v_1 = 0\, m/s$, $v_2 = 1\, m/s$