Equation frac{{dV}}{{dt}} = At - BV is describing rate of change of velocity of a body falling

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1.Units, Dimensions and Measurement

medium

The equation $\frac{{dV}}{{dt}} = At - BV$ is describing the rate of change of velocity of a body falling from rest in a resisting medium. The dimensions of $A$ and $B$ are

A

$LT^{-3}, T$

B

$LT^{-3}, T^{-1}$

C

$LT, T$

D

$LT, T^{-1}$

Solution

Given, $\mathrm{dv} / \mathrm{dt}=\mathrm{At}-\mathrm{Bv}$

Here, dv/dt is rate of change of velocity, v is velocity and t is time.

So, dimension of $A=\left[L T^{-2}\right] /[T]=\left[L T^{-1}\right]$

$\therefore$ dimension of $\mathrm{A}=\left[\mathrm{L} T^{-3}\right]$

Dimension of $\mathrm{B}=\left[\mathrm{L} T^{-2}\right] /\left[\mathrm{L} T^{-1}\right]=\left[\mathrm{T}^{-1}\right]$

$\therefore$ dimension of $\mathrm{B}=\left[\mathrm{T}^{-1}\right]$

Standard 11

Physics

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