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

The Correct Option is B

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 $Q$.

Answer 2

Step 1: Understand Rolling Motion 

In rolling motion, a point on the rim of the wheel has both rotational and translational motion. The velocities due to both these motions add vectorially.

Step 2: Analyze the Velocity at Points P and Q

• Point P is at the top of the wheel. Its velocity is the sum of the linear speed (v) of the wheel and the rotational speed (v).
• Point Q is at the bottom of the wheel, where the linear speed (v) and rotational speed (-v) cancel out.

Step 3: Calculate Velocities

Velocity at P:

$$ v_P = v + v = 2v $$

Velocity at Q:

$$ v_Q = v - v = 0 $$

Step 4: Conclusion

Point P moves faster than Point Q, and Point Q has zero velocity.