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  4. 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.

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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 ____$ms ^{-1}$.

JEE MainJEE Main 2023System of Particles and Rotational Motion

Solution:

$ KE =\frac{1}{2} mv ^2+\frac{1}{2} I \omega^2 $
$ 2240=\frac{1}{2} 2( v )^2+\frac{1}{2} \frac{2}{5}(2) R ^2 \cdot\left(\frac{ v }{ R }\right)^2 $
$2240= v ^2+\frac{2}{5} v ^2$
$ \Rightarrow v =40 \,m / s $