Question

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) ?

• A. Point P moves slower than point Q.
• B. Point P moves faster than point Q
• C. Both the points P and Q move with equal speed.
• D. Point P has zero speed.

Answer 1

Answer: (B)

Point P moves faster than point Q

Answer 2

The velocity of a point on a rolling wheel is the vector sum of the linear velocity of the
wheel's center and the tangential velocity of the point due to rotation.
For the topmost point $P$, the tangential velocity due to rotation is in the same direction as the linear velocity.
Thus, its speed is $v + v = 2v$.
For the bottommost point $Q$, the tangential velocity is opposite to the linear velocity, resulting in a net speed of $v - v = 0$.
Thus, point $P$ moves faster than point $Q$.