question_answer

A steel ball of radius 2 cm is at rest on a frictionless surface. Another ball of radius 4cm moving at a velocity of 81 cm/sec collides elastically with first ball. After collision the smaller ball moves with speed of                                       [RPMT 1999]

A)          81 cm/sec

B)                       63 cm/sec

C)          144 cm/sec

D)                       None of these

Correct Answer: C

Solution :

         Ratio in radius of steel balls = 1/2 So, ratio in their masses\[=\frac{1}{8}\]                                [As\[M\propto V\propto {{r}^{3}}\]]               Let \[{{m}_{1}}=8m\] and \[{{m}_{2}}=m\] \[{{v}_{2}}=\frac{2{{m}_{1}}{{u}_{1}}}{{{m}_{1}}+{{m}_{2}}}=\frac{2\times 8m\times 81}{8m+m}=144\,cm/s\]