Question

A solid cylinder of mass 50 kg and radius 0.5 m is free to rotate about the horizontal axis . A massless string is wound round the cylinder with one end attached to it and other hanging freely. Tension in the string required to produce an angular acceleration of 2 revolutions $ s^ {-2} $ is

• A. 25 N
• B. 50 N
• C. 78.5 N
• D. 157 N

Answer 1

The Correct Option is D

Here, mass of the cylinder, M = 50 kg
Radius of the cylinder, R = 0.5 m
Angular acceleration, $ \alpha = 2\, rev\, s^{-2} $
$ 2 \times 2 \pi \,rad\, s^{-2} = 4 \pi\, rad\,s^{-2} $
Torque, $\tau = TR $
Moment of inertia of the solid cylinder about its axis, $ I = \frac{1}{2} MR^2 $
$ \therefore $ Angular acceleration of the cylinder
$ \alpha = \frac{\tau}{1} = \frac{TR}{\frac{1}{2}MR^2} $
$ T = \frac{MR\alpha}{2} = \frac{50 \times 0.5 \times 4 \pi}{2} = 157 N $