A solid sphere of mass 1 kg rolls without slipping on a plane surface. Its kinetic energy is 7 × 10 - 3 J . The speed of the centre of mass of the sphere is ______ cm s - 1 .

Question

TestHub · Accepted Answer

Let velocity of centre of mass of sphere be $v$ .

Total kinetic energy of solid sphere is $K E = \frac{1}{2} m v^{2} + \frac{1}{2} I ω^{2}$ , where, $I$ is moment of inertia of the solid sphere about the axis passing through it's centre of mass and $ω = \frac{v}{R} (pure rolling condition)$ .

Therefore,

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

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

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

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

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