A solid sphere of mass 2 kg is making pure rolling on a horizontal surface with kinetic energy 2240 J. The velocity of centre of mass of the sphere will be ______ . [2023]

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Solution

Q.
A solid sphere of mass 2 kg is making pure rolling on a horizontal surface with kinetic energy 2240 J. The velocity of centre of mass of the sphere will be ______ ${ms}^{- 1}$ . [2023]

Ans.
(40)

$K E = \frac{1}{2} m v^{2} + \frac{1}{2} I ω^{2}$

$2240 = \frac{1}{2} 2 {(v)}^{2} + \frac{1}{2} (\frac{2}{5}) (2) R^{2} \cdot {(\frac{v}{R})}^{2}$

$2240 = v^{2} + \frac{2}{5} v^{2}$

$\Rightarrow v = 40 m/s$

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