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NEET PHYSICSEasy

A wheel of a bullock cart is rolling on a level road as shown in the figure below. If its linear speed is vv in the direction shown, which one of the following options is correct (PP and QQ are any highest and lowest points on the wheel, respectively)?

A

Point PP moves faster than point QQ.

B

Both the points PP and QQ move with equal speed.

C

Point PP has zero speed.

D

Point PP moves slower than point QQ.

Step-by-Step Solution

In pure rolling motion, the velocity of any point on the wheel is the vector sum of the translational velocity of the center of mass (vv) and the tangential velocity due to rotation (ωR\omega R). For a wheel of radius RR rolling without slipping, the condition is v=ωRv = \omega R. At the highest point PP, the translational velocity and rotational velocity are in the same direction. So, the net speed is vP=v+ωR=v+v=2vv_P = v + \omega R = v + v = 2v. At the lowest point QQ (point of contact with the ground), the translational velocity and rotational velocity are in opposite directions. So, the net speed is vQ=vωR=vv=0v_Q = v - \omega R = v - v = 0. Therefore, point PP moves with a speed of 2v2v, while point QQ is instantaneously at rest (speed is zero). Thus, point PP moves faster than point QQ.

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