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

The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are
  1. $\mathrm{kg} \mathrm{ms}^{-1}$
  2. $\mathrm{kg} \mathrm{ms}^{-2}$
  3. $\mathrm{kg} \mathrm{s}^{-1}$
  4. $\mathrm{kg} \mathrm{s}$

Solution

Given, Damping force $\propto$ velocity
$\begin{aligned}
& F \propto y \\
& F=k v \\
& k=\frac{F}{v}
\end{aligned}$
$\begin{aligned}
\text {Unit of } k & =\frac{\text { unit of } F}{\text { unit of } v} \\
& =\frac{\mathrm{kg}-\mathrm{ms}^{-2}}{\mathrm{~ms}^{-1}}=\mathrm{kgs}^{-1}
\end{aligned}$

Asked in: NEET 2012 (Screening)

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