Physics

# The velocity $v$ of a particle at time$t$ is given by $\displaystyle v = at + \frac {b} {t + c}$ where $a, b$ and $c$ are constants. The dimensions of $a, b$ and $c$ are respectively :

$LT^{-2}\, , L$ and $\displaystyle T$

##### SOLUTION

According to the principle of dimensional homogenity

Dimension of v = dimension of at  =  dimension of $\displaystyle \frac {b} {t +c}$

Dimension of a =  $\displaystyle \frac {[v]} {[t]} = \frac {LT^{-2}} {T} = [LT^{-2}]$

Dimension of b = $\displaystyle [v] [t] = [LT^{-1}T] = [L]$

Dimension of c = $\displaystyle [t] = [T]$

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Single Correct Medium Published on 18th 08, 2020
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