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Q.

A Wheel of radius R and mass M is placed at the bottom of fixed step 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?

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a

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

b

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

c

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

d

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

answer is A.

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Detailed Solution

(A) →  net torque, when F acts at P is zero, as it intersects axis of rotation. (B) → If the force is applied tangentially at point S then τ≠0 and the wheel climbs the step. (C) →If the force is applied at the point P tangentially then τ remains constant. (D) →If the force is applied normal to the circumference at point X then the length of perpendicular from Q           on the line of force remains constant as the wheel just climbs up, so torque remains constant.
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A Wheel of radius R and mass M is placed at the bottom of fixed step 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?