A smooth sphere of mass m, moving with velocity u on a surface, collides with another smooth sphere of same size but of mass 2m. The velocity range of second sphere after collision will be

v > \frac{2 u}{3}

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v < \frac{u}{3}

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v = u

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\frac{u}{3} \leq v \leq \frac{2 u}{3}

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Solution

The correct option is D $\frac{u}{3} \leq v \leq \frac{2 u}{3}$
Let us consider this collision to be head on.
Purely inelastic:
$v_{2} = v_{C O M} = m u / 3 m = u / 3$
Purely elastic:
$v_{2} = (2 m_{1} / m_{1} + m_{2}) u_{1}$ (since $u_{2}$ = 0)
general elastic collision equation
$v_{2} = 2 u / 3$
Thus speed of 2m lies between u/3 and 2u/3

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