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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?

640606_a9a2c04c139b4bad8596f7347ac04c4c.png

A
If the force is applied tangentially at point S then τ0 but the wheel never climbs the step
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B
If the force is applied normal to the circumference at point P then τ is zero
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C
If the force is applied normal to the circumference at point X then τ is constant
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D
If the force is applied at point P tangentially then τ decreases continuously as the wheel climbs
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Solution

The correct options are
A If the force is applied normal to the circumference at point P then τ is zero
C If the force is applied normal to the circumference at point X then τ is constant
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.

682789_640606_ans_c080c522c0194bcb86e1559aeb8e4754.PNG

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