A wheel of radius and mass is placed at the bottom of a fixed step of height as shown in the figure. [2017]

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 [2017]

Smart Achievers · Accepted Answer

(3)

If the force $(F)$ is applied at P tangentially then the torque remains constant and $τ = F \times 2 R$ .

If force is applied normal to X, then as the wheel climbs, then the perpendicular distance of force from Q will go on changing initially the perpendicular distance is QM, later it becomes QM'.

If the force (F) is applied normal to the circumference at point P then $τ = 0$ .

If the force (F) is applied tangentially at point S then $τ = F \times R$ and the wheel climbs.

Solution

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

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

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

4 If the force is applied tangentially at point $S$ then $τ \neq 0$ but the wheel never climbs the step

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Solution

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

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

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

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

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

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

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

4 If the force is applied tangentially at point $S$ then $τ \neq 0$ but the wheel never climbs the step