Question

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

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

Answer 1

Answer: (B)

Given, mass of disc $=M$
Radius of disc $=R$
We know that,
$\tau =I\alpha ...(i)$
But $\tau =F\times R$
$I=\frac{M{R}^2}{2}$
and $\alpha =\frac{\omega }{t}$
Therefore, $F\times R=\frac{M{R}^2}{2}\times \frac{\omega }{t}$
$F=\frac{MR}{2}\times \frac{\omega }{t}F=\frac{MR\omega }{2t}$