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

Answer: (B), (C)

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

A: Torque due to $mg$ decreases with angle whereas torque due to force is minimum at initial state.

B: Applied force passes through point $Q$. So, its torque is zero.

$\because {\overrightarrow{r}}_{PQ}\times \overrightarrow{f}=0$. Hence $\tau$ is zero

C: Torque due to applied force at $X$ remains constant. The perpendicular distance to the line of the force remains constant. Hence torque remains constant.

D: If the force is applied at the point $P$ tangentially then $\tau$ remains constant.