Question

The damping force of an oscillator is directly proportional to the velocity. The unit of constant of proportionality is

• A. \( \text{kg} \, \text{m} \, \text{s}^{-2} \)
• B. \( \text{kg} \, \text{s}^{-1} \)
• C. \( \text{kg} \, \text{m} \, \text{s}^{-1} \)
• D. \( \text{kg} \, \text{s} \)

Hint:

For damping forces, the constant of proportionality has units of \( \text{kg} \, \text{s}^{-1} \), representing the resistance to motion of an oscillator.

Answer 1

The Correct Option is B

Step 1: Damping force.
The damping force \( F_d \) is proportional to the velocity \( v \) of the oscillator. This can be written as: \[ F_d = -b v \] where \( b \) is the damping constant, and its unit must match the unit of force (N) divided by the unit of velocity (m/s).
Step 2: Unit analysis.
The unit of force is \( \text{kg} \, \text{m} \, \text{s}^{-2} \), and the unit of velocity is \( \text{m} \, \text{s}^{-1} \). Therefore, the unit of \( b \) is: \[ \text{Unit of } b = \frac{\text{kg} \, \text{m} \, \text{s}^{-2}}{\text{m} \, \text{s}^{-1}} = \text{kg} \, \text{s}^{-1} \]
Step 3: Conclusion.
The unit of the constant of proportionality is \( \text{kg} \, \text{s}^{-1} \), so the correct answer is (B).