Question

A circular disc of radius R is free to rotate about an axis passing through its centre. An external tangential force F is applied on the disc along its edge. If the angular velocity of disc is increased from 0 to ωin a time t then the work done by F during same time t is

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

We know that ${\omega }_f^2-{\omega }_i^2=2\alpha \theta$

$\Rightarrow {\omega }^2-o^2=2\alpha \theta \Rightarrow \theta =\frac{{\omega }^2}{2\alpha }\to \left(1\right)$

As${\omega }_f={\omega }_i+\alpha t\Rightarrow \omega =\alpha =\frac{\omega }{t}\to \left(2\right)$

From (1) & (2) $\theta =\frac{\omega t}{2}$

$\therefore$ Work done $\left(W\right)=\tau \theta$

$\Rightarrow W=\left(F\right)\left(R\right)(\frac{\omega t}{2})$

$\Rightarrow W=\frac{RF\omega t}{2}$