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?

Step-by-step solution

(i) is incorrect. If force is applied normal to surface at point X τ = F y R sin ⁡ θ Thus τ depends on θ and it is not constant (ii) is incorrect If force applied tangentially at S τ = F × R ≠ 0 But it will climb as mentioned in question. If force is applied normal to surface at P then line of action of force will pass from Q and thus τ = 0 (iv) is incorrect. If force is applied at P tangentially the τ = F × 2 R = c o n s t a n t