Question

A cord of negligible mass is wound around the rim of a wheel supported by spokes with negligible mass. The mass of the wheel is 10 kg and radius is 10 cm and it can freely rotate without any friction. Initially the wheel is at rest. If a steady pull of 20 N is applied on the cord, the angular velocity of the wheel, after the cord is unwound by 1 m, will be:

• A. 20 rad/s
• B. 30 rad/s
• C. 10 rad/s
• D. 0 rad/s

Hint:

When a steady force is applied and the object rotates, the work done on the object is equal to its kinetic energy.

Answer 1

The Correct Option is A

The work performed by the force \( F = 20 \, N \) is calculated as: \[ W_f = F \cdot d = 20 \times 1 = 20 \, J \] This work represents the change in the wheel's kinetic energy: \[ KE = \frac{1}{2} I \omega^2 \] The moment of inertia \( I \) is determined using \( I = MR^2 \), with \( M = 10 \, \text{kg} \) and \( R = 0.1 \, \text{m} \): \[ I = 10 \times (0.1)^2 = 0.1 \, \text{kg m}^2 \] Equating the work done to the change in kinetic energy allows us to solve for \( \omega \): \[ 20 = \frac{1}{2} \times 0.1 \times \omega^2 \quad \Rightarrow \quad \omega = 20 \, \text{rad/s} \]