Question

A torque of 10 Nm is applied on a wheel having angular momentum of 2 kg m\(^2\) s\(^{-1}\). The angular momentum of the wheel after 4 s is:

• A. 40 kg m\(^2\) s\(^{-1}\)
• B. 42 kg m\(^2\) s\(^{-1}\)
• C. 4 kg m\(^2\) s\(^{-1}\)
• D. 4.2 kg m\(^2\) s\(^{-1}\)

Hint:

The change in angular momentum is equal to the torque multiplied by time.

Answer 1

The Correct Option is B

The angular momentum is related to the applied torque by the equation: \[ L = L_0 + \tau t \] Where: - \( L_0 = 2 \, {kg} \cdot {m}^2 \, {s}^{-1} \) is the initial angular momentum, - \( \tau = 10 \, {Nm} \) is the applied torque, - \( t = 4 \, {s} \) is the time for the torque application. 
Substituting the values: \[ L = 2 + (10 \times 4) = 2 + 40 = 42 \, {kg} \cdot {m}^2 \, {s}^{-1} \] Final Answer: 42 kg m\(^2\) s\(^{-1}\)