Question: 32. A wheel of a bullock cart is rolling on a level road as shown in the figure below. If its linear speed is v in the direction shown, which one of the following options is correct (P and Q are any highest and lowest points on the wheel, respectively) ?
(1) Point P moves slower than point Q .
(2) Point P moves faster than point Q.
(3) Both the points P and Q move with equal speed.
(4) Point P has zero speed.
Answer: Option (2)
Explanation:
For a wheel rolling without slipping, the velocity of any point is the vector sum of translational velocity of the centre and rotational velocity about the centre.
The translational velocity of the centre of the wheel is v in the forward direction.
The magnitude of the rotational velocity at the rim is also v,
since v = \omega R.
At the topmost point P,
the rotational velocity is in the same direction as the translational velocity.
Hence, the speed of point P is
v_P = v + v = 2vAt the bottommost point Q,
the rotational velocity is opposite to the translational velocity.
Hence, the speed of point Q is
v_Q = v - v = 0Therefore, point P moves faster than point Q.
Thus, the correct answer is Option (2).