JEE Main · 2023 · 29 Jan 2023 · Shift 1 · Rotational Mechanics

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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}

Answer: 40

Solution

A rolling solid sphere carries translational and rotational energy, and with

I = \frac{2}{5} m R^{2}

and

ω = \frac{v}{R}

the total is

K E = \frac{1}{2} m v^{2} + \frac{1}{5} m v^{2} = \frac{7}{10} m v^{2}

. Setting

\frac{7}{10} (2) v^{2} = 2240

gives

v^{2} = 1600

. The centre of mass moves at

40

m s

^{- 1}

JEE Main · 2023 · 29 Jan 2023 · Shift 1 · Integer answer

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