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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 τ about an axis normal to the plane of the paper passing through the point Q. Which of the following options is/are correct?

If the force is applied normal to the circumference at point P then τ is zero

If the force is applied at point P tangentially then τ decreases continuously as the wheel climbs

If the force is applied tangentially at point S then τ ≠ 0 but the wheel never climbs the step

If the force is applied normal to the circumference at point X then τ is constant

Solution:

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. ⇀rPQ × ⇀f = 0. Hence τ 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 τ remains constant.