Question

A solid sphere of mass $M$ and radius $R$ spins about an axis passing through its centre making $600 \mathrm{rpm}$. Its kinetic energy of rotation is (a) $\frac{2}{5} \pi^{2} M R$ (b) $\frac{2}{5} \pi M^{2} R^{2}$ (c) $80 \pi^{2} M R^{2}$ (d) $80 \underline{\pi} R$

Name: Problem 20, Chapter 9: Master Resource Book in JEE Main Physics
Uploaded: 2022-01-14T13:44:34-08:00
Duration: 57 s
Channel: Hast Aggarwal
Description: A solid sphere of mass M and radius R spins about an axis passing through its centre making 600 rpm. Its kinetic energy of rotation is (a) (2)/(5) π^2 M R (b) (2)/(5) πM^2 R^2 (c) 80 π^2 M R^2 (d) 80 π R

   A solid sphere of mass $M$ and radius $R$ spins about an axis passing through its centre making $600 \mathrm{rpm}$. Its kinetic energy of rotation is
(a) $\frac{2}{5} \pi^{2} M R$
(b) $\frac{2}{5} \pi M^{2} R^{2}$
(c) $80 \pi^{2} M R^{2}$
(d) $80 \underline{\pi} R$

Master Resource Book in JEE Main Physics

D. B. Singh 1st Edition

Chapter 9, Problem 20

Instant Answer

Solved by Expert Hast Aggarwal

01/14/2022

Step 1

E = \frac{1}{2}I\omega^{2}$, where $I$ is the moment of inertia and $\omega$ is the angular velocity. Show more…

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A solid sphere of mass $M$ and radius $R$ spins about an axis passing through its centre making $600 \mathrm{rpm}$. Its kinetic energy of rotation is (a) $\frac{2}{5} \pi^{2} M R$ (b) $\frac{2}{5} \pi M^{2} R^{2}$ (c) $80 \pi^{2} M R^{2}$ (d) $80 \underline{\pi} R$

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Key Concepts

Rotational Kinetic Energy

Rotational kinetic energy is the energy possessed by a rotating object due to its motion, analogous to translational kinetic energy. It is calculated using the formula K = 1/2 I ?², where I is the moment of inertia and ? is the angular velocity.

Moment of Inertia

The moment of inertia quantifies how the mass of an object is distributed relative to the axis of rotation, affecting its resistance to changes in rotational motion. For a solid sphere about an axis through its center, the moment of inertia is given by I = (2/5)MR², where M is the mass and R is the radius.

Angular Velocity Conversion

Angular velocity is typically measured in radians per second in physics calculations. Converting from revolutions per minute (rpm) to radians per second involves multiplying by 2? and dividing by 60, since one revolution is 2? radians and there are 60 seconds in one minute.

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