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 $'\omega '$ 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

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{M R}{2} \times \frac{\omega}{t} \,\,\,\, F=\frac{M R \omega}{2 t} $