Question

A uniform solid cylinder of mass 'M' and radius 'R' is resting on a horizontal platform (which is parallel to X-Y plane) with its axis along the Y-axis and free to roll on the platform. The platform is given a motion in X-direction given by $x=A\cos \omega t$. There is no slipping between the cylinder and the platform. The maximum torque acting on the cylinder as measured about its centre of mass is

• A. $\frac{1}{2}MRA{\omega }^2$
• B. $MRA{\omega }^2$
• C. $2mRA{\omega }^2$
• D. $mRA\omega A^2{\cos }^2\omega t$

Answer 1

The correct option is A $\frac{1}{2}MRA{\omega }^2$

$\overrightarrow{\tau }=I\alpha =\frac{1}{2}M{R}^2\times \left(\frac{Linearacceleration}{R}\right)$
acceleration = ${\omega }^{2}A\sin \omega t$ or $(linearacceleration{)}_{max}={\omega }^{2}A$
$\therefore (\tau {)}_{max}=\frac{1}{2}\frac{M{R}^2{\omega }^2}{R}=\frac{1}{2}MRA{\omega }^2.$