Question: The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are: [PMT/NEET-2012]
a. kg m s$^{-1}$
b. kg m s$^{-2}$
c. kg s$^{-1}$
d. kg s

Answer: The correct answer is: c. kg s⁻¹

Explanation:
For a damped oscillator, the damping force is

$
F = -b v
$

where

• $F$ = damping force (N = kg·m·s⁻²)
• $v$ = velocity (m·s⁻¹)
• $b$ = damping constant

So,
$
[b] = \frac{F}{v} = \frac{kg \, m \, s^{-2}}{m \, s^{-1}}
$

Simplifying,
$
[b] = kg \, s^{-1}
$

Hence, the unit of the damping constant is kg s⁻¹.