Question

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

• A. $\left[LT^{-2}\right]$, $\left[L\right]$ and $\left[T\right]$
• B. $\left[L^{2}\right]$, $\left[T\right]$ and $\left[LT^{2}\right]$
• C. $\left[LT^{2}\right]$, $\left[LT\right]$ and $\left[L\right]$
• D. $\left[L\right]$, $\left[LT\right]$ and $\left[T^{2}\right]$

Answer 1

Answer: (A)

$v=a t+\frac{b}{t+c}$
As $c$ is added to $t, $
$\therefore [c]=[ T ]$
$[a t]=\left[ LT ^{-1}\right] $
or, $[a]=\frac{\left[ LT ^{-1}\right]}{[ T ]}=\left[ LT ^{-2}\right] $
$\frac{[b]}{[ T ]}=\left[ LT ^{-1}\right] $
$ \therefore[b]=[ L ] $.