Question

A disc has 'M' and radius 'R'. How much tangential force should be applied to the rim of the disc so as to rotate with angular velocity '\omega' in time 't'?

• A. $\frac{MR\omega }{4t}$
• B. $\frac{MR\omega }{2t}$
• C. $\frac{MR\omega }{t}$
• D. $MR\omega t$

Answer 1

The correct option is B $\frac{MR\omega }{2t}$

Angular acceleration, $\alpha =\frac{\omega }{t}$

And, moment of inertia of disc $I=\frac{1}{2}M{R}^2$

Hence, torque, $\tau =I.\alpha =\frac{1}{2}M{R}^2\frac{\omega }{t}$

$\tau =F.R$

$⟹F=\frac{\tau }{R}$

$⟹F=\frac{MR\omega }{2t}$

Hence, correct answer is option-(B).