A solid sphere of mass 1 kg rolls without slipping on a plane surface. Its kinetic energy is 7×10−5J. The speed of the center of mass of the sphere is_________ cms-1.

K⋅ERool =K⋅Etroms +K⋅ERot 7×10−5=12mv2+1225mR2V2R2=12mv2+15mv2 7×10−5=710mv2 7×10−5=710×1×v2 v2=10−4 v=0.01m/s=1cm/s

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A solid sphere of mass 1 kg rolls without slipping on a plane surface. Its kinetic energy is $7 \times 10^{- 5} J$ . The speed of the center of mass of the sphere is_________ cms^-1.

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Detailed Solution

$\begin{array}{l} K \cdot E_{Rool} = K \cdot E_{troms} + K \cdot E_{Rot} \\ 7 \times 10^{- 5} = \frac{1}{2} {mv}^{2} + \frac{1}{2} [\frac{2}{5} {mR}^{2}] \frac{V^{2}}{R^{2}} \\ = \frac{1}{2} {mv}^{2} + \frac{1}{5} {mv}^{2} \\ 7 \times 10^{- 5} = \frac{7}{10} {mv}^{2} \begin{aligned} 7 \times 10^{- 5} = \frac{7}{10} \times 1 \times v^{2} \\ \begin{aligned} v^{2} = 10^{- 4} \\ v = 0.01 m / s = 1 cm / s \end{aligned} \end{aligned} \end{array}$

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