A solid sphere of mass 1 kg rolls without slipping on a plane surface. Its kinetic energy is J. The speed of the centre of mass of the sphere is ______ cm . [2023]

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Solution

Q.
A solid sphere of mass 1 kg rolls without slipping on a plane surface. Its kinetic energy is $7 \times 10^{- 3}$ J. The speed of the centre of mass of the sphere is ______ cm $s^{- 1}$ . [2023]

Ans.
(10)

$\frac{1}{2} m v^{2} + \frac{1}{2} I ω^{2} = 7 \times 10^{- 3}$

$\frac{1}{2} m v^{2} + \frac{1}{2} (\frac{2}{5} M R^{2}) {(\frac{v}{R})}^{2} = 7 \times 10^{- 3}$

$\frac{1}{2} M v^{2} [1 + \frac{2}{5}] = 7 \times 10^{- 3}$

$\frac{1}{2} (1) (v^{2}) (\frac{7}{5}) = 7 \times 10^{- 3}$

$v^{2} = 10^{- 2}$

$v = 10^{- 1} = 0.1 m/s = 10 cm/s$

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