Question

The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are

• A. $kg\,ms^{-1}$
• B. $kg\,ms^{-2}$
• C. $kg\,s^{-1}$
• D. $kg\,s$

Answer 1

The Correct Option is C

To determine the units of the constant of proportionality for the damping force on an oscillator, we must first understand the relationship between the damping force and velocity. The problem states that the damping force is directly proportional to the velocity. Mathematically, this can be expressed as:

F_d = -b \cdot v

where:

• F_d is the damping force.
• b is the constant of proportionality (also known as the damping coefficient).
• v is the velocity of the oscillator.

We need to find the units of b given that the units of force are N (Newton), and 1 Newton is equal to 1 \, kg \cdot m \cdot s^{-2}. The unit of velocity is m \cdot s^{-1}.

Substituting the units into the formula, we have:

[b] \cdot [v] = [F_d]

[b] \cdot (m \cdot s^{-1}) = kg \cdot m \cdot s^{-2}

Solving for the units of b:

[b] = \frac{kg \cdot m \cdot s^{-2}}{m \cdot s^{-1}}

[b] = kg \cdot s^{-1}

Thus, the unit of the constant of proportionality b is kg \cdot s^{-1}.

Therefore, the correct answer is kg \cdot s^{-1}.