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  4. A sphere of mass m moving with velocity v collides head-on another sphere of same mass which is at rest. The ratio of final velocity of the second sphere to the initial velocity of the first sphere is ( e is the coefficient of restitution and collision is inelastic)

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Q. A sphere of mass $m$ moving with velocity $v$ collides head-on another sphere of same mass which is at rest. The ratio of final velocity of the second sphere to the initial velocity of the first sphere is ( $e$ is the coefficient of restitution and collision is inelastic)

NTA AbhyasNTA Abhyas 2020

Solution:

Solution
$m u + 0 = m u_{1} + m u_{2}$
$\upsilon_{1} + \upsilon_{2} = \upsilon$ ....(i)

$e = \frac{\upsilon_{2} - \upsilon_{1}}{\upsilon - 0}$
$e \upsilon = \upsilon_{2} - \upsilon_{1}$ ..(ii)
Add equation (i) & equation (ii)
$e \upsilon + \upsilon = 2 \upsilon_{2}$
$\left(\upsilon\right)_{2} = \frac{\upsilon \left(\right. e + 1 \left.\right)}{2}$
$\frac{\upsilon_{2}}{\upsilon} = \frac{e + 1}{2}$