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Q.

A solid sphere is set into motion on a rough horizontal surface with a linear speed V in the forward direction and an angular speed V/R in the anti clock wise direction as shown in figure. Find the linear speed of the sphere when slipping finally ceases and pure rolling starts?

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a

$\frac{6 V}{7}$

b

$\frac{2 V}{5}$

c

$\frac{4 V}{7}$

d

$\frac{3 V}{7}$

answer is B.

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Detailed Solution

As there is no external torque, angular momentum is a constant. L_i = L_f
$\begin{array}{l} mVR - Iω = {mV}^{1} R + {Iω}^{1} \\ mVR - \frac{2}{5} {mR}^{2} \cdot \frac{V}{R} = {mV}^{1} R + \frac{2}{5} {MR}^{2} \cdot \frac{V^{1}}{R} \\ V - \frac{2 V}{5} = V^{1} + \frac{2 V^{1}}{5} \\ \frac{3 V}{5} = \frac{7 V^{1}}{5} V^{1} = \frac{3 V}{7} \end{array}$

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