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MHT CET 2021 (22 Sep, Shift 1) · Rotational Kinetic Energy, Work & Power

Rotational Kinetic Energy, Work & Power question from MHT CET 2021 (22 Sep, Shift 1)

Q36MHT CET 2021 · 22 SEP · SHIFT 1Medium

Rotational Kinetic Energy, Work & Power

A solid sphere of mass ' $M$ ' and radius ' $R$ ' is rotating about its diameter. A solid cylinder of same mass and same radius is also rotating about its geometrical axis with an angular speet twice that of the sphere. The ratio of the kinetic energy of rotation of the sphere to that of the cylinder is

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Answer: (b)

Sphere: $K_s = \frac{1}{2}\left(\frac{2}{5}MR^2\right)\omega^2 = \frac{MR^2\omega^2}{5}$
Cylinder at $2\omega$ : $K_c = \frac{1}{2}\left(\frac{1}{2}MR^2\right)(4\omega^2) = MR^2\omega^2$
$\frac{K_s}{K_c} = \frac{1}{5}$
So the answer is (b) $1 : 5$ .

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