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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 $$\tau$$ 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 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 $$\tau$$ is zero
C If the force is applied normal to the circumference at point X then $$\tau$$ 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.
$$\because \vec{r}_{PQ} \times \vec{f} = 0$$. Hence $$\tau$$ 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 $$\tau$$ remains constant.

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Physics

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