A solid sphere and hollow sphere of the same mass and radius are given a spin about their centre of mass and then, they are placed on a rough horizontal surface. The spin angular velocity is the same

Question

A solid sphere and hollow sphere of the same mass and radius are given a spin about their centre of mass and then, they are placed on a rough horizontal surface. The spin angular velocity is the same for both the spheres and it is equal to ω 0 . Once the pure rolling starts; let v 1 and v 2 be the linear speeds of their centres of mass, then

TestHub · Accepted Answer

From conservation of angular momentum about point of contact :

$I ω_{0} = I ω + mRv$
or $I ω_{0} = I \frac{v}{R} + mRv$
or $v = \frac{I ω_{0}}{\frac{I}{R} + mR}$
or
or $v = \frac{ω_{0}}{\frac{1}{R} + \frac{mR}{I}}$
Now $I_{solid sphere <} I_{hollow}$
∴ $v_{solid <} v_{hollow}$
∴ $v_{1} < v_{2}$

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