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 clims 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?

Options

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

Answer

A, C

Explanation

(i) If force is applied normal to surface at P, then line of action of force will pass from Q and thus. `tau=0`.
(ii) Wheel can climb.

(iii) `tau = F(2R cos theta) - mg R cos theta, tau propto cos theta`.

Hence, as `theta` increases,
`tau` decreases,
So its correct.
(iv)
`tau =Fr -mg cos theta, tau` increases with `theta`.