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

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

Solution

$\begin{array}{l} \mathrm{F}=\mathrm{bv} \\ \mathrm{b}=\frac{\mathrm{F}}{\mathrm{v}}=\frac{\mathrm{N}}{\mathrm{m} / \mathrm{s}}=\frac{\mathrm{MLT}^{-2}}{\mathrm{~L}} \mathrm{~T}=\mathrm{ML}^{-1} \\ \Rightarrow \mathrm{kg} \mathrm{sec}^{-1} \end{array}$

Asked in: MHT CET 2020 (16 Oct Shift 2)

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