Work Energy and Power - Result Question 55
58. 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:
[2010]
(a) 0,1
(b) 1,1
(c) $1,0.5$
(d) 0,2
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Answer:
Correct Answer: 58. (a)
Solution:
- (a) Clearly $v_1=2 ms^{-1}, v_2=0$
$m_1=m$ (say), $m_2=2 m$
$v_1{ }^{\prime}=?, v_2^{\prime}=$ ?
$e=\frac{v_1^{\prime}-v_2^{\prime}}{v_2-v_1}$
By conservation of momentum,
$2 m=m v_1{ }^{\prime}+2 m v_2{ }^{\prime}$
From (i),
$0.5=\frac{v_2{ }^{\prime}-v_1{ }^{\prime}}{2}$
$\therefore v_2{ }^{\prime}=1+v_1{ }^{\prime}$
From (ii),
$ \begin{aligned} & 2=v_1^{\prime}+2+2 v_1^{\prime} \\ \Rightarrow & v_1^{\prime}=0 \text{ and } v_2^{\prime}=1 ms^{-1} \end{aligned} $
