Question

The solid cylinder depicted above with moment of inertia, $I$, is being acted on by force, $F$, that acts tangentially along the edge of the disc as depicted above.
What must be the value of force $F^{\prime }$ so that the cylinder rotates at a constant angular velocity if $r=\frac{R}{2}$.

• A. $F^{\prime }=2F$
• B. $F^{\prime }=\frac{F}{2}$
• C. $F^{\prime }=F$
• D. $F^{\prime }=2F\sin \left({30}^o\right)$
• E. $F^{\prime }=\frac{F}{2}\sin \left({30}^o\right)$

Answer 1

The correct option is A $F^{\prime }=2F$

As the solid cylinder rotates at constant angular velocity, thus its angular acceleration is zero i.e $\alpha =0$

Using $\tau =I\alpha$ $⟹\tau =0$

Thus net torque about centre of cylinder must be equal to zero.

$\therefore$ $F^{\prime }r-FR=0$

OR $F^{\prime }\times \frac{R}{2}=FR$ $⟹F^{\prime }=2F$