Question

A wheel of radius $R$ and mass $M$ is placed at the bottom of a fixed step of height $R$ as shown in the figure. A constant force is continuously applied on the surface of the wheel so that it just climbs the step without slipping. Consider the torque $\tau$ about an axis normal to the plane of the paper passing through the point $Q$. Which of the following options is/are correct?

• A. If the force is applied tangentially at point $S$ then $\tau \ne 0$ but the wheel never climbs the step
• B. If the force is applied normal to the circumference at point P then $\tau$ is zero
• C. If the force is applied normal to the circumference at point X then $\tau$ is constant
• D. If the force is applied at point P tangentially then $\tau$ decreases continuously as the wheel climbs

Answer 1

The correct option is B

If the force is applied normal to the circumference at point P then $\tau$ is zero

A:
As we increase the force applied at point $S$, torque about $Q$ increases and once it is more than the torque due to weight of body about $Q$ the wheel will climb the step. So, option 'A' is incorrect

B:
Applied force passes through point $Q$. So, its torque is zero.
(Torque due to gravity is balanced by the normal reaction force.)

Hence $\tau =0$

C:


Torque due to applied force at $X$ remains constant. The perpendicular distance to the line of the force remains constant. But torque due to gravity decreases continuously.
Hence $\tau$ changes.
Hence 'C' is incorrect.

D:
If the force is applied at the point $P$ tangentially then $\tau$ due to applied force remains constant, but torque due to gravity decreases which in turn increases net torque about $Q$.
So, option 'D' is incorrect.