Question

The velocity $v$ (in $cm / s$ ) of a particle is given in terms of time $t$ (in seconds) by the equation,
$v=a t+\frac{b}{t+c}$
The dimensions of $a, b$ and $c$ are :

• A. a- $ [L^{2}] $ b- $ [T] $ c- $ [LT^{2}] $
• B. a- $ [LT^{2}] $ b- $ [LT] $ c- $ [L] $
• C. a -$ [LT^{-2}] $ b- $ [L] $ c- $ [T] $
• D. a -$ [L] $ b -$ [LT] $ c -$ [T^{2}] $

Answer 1

Answer: (C)

$v =a t+\frac{b}{t+c} $
$[a t] =[v]=\left[ LT ^{-1}\right]$
$\therefore [a] =\frac{\left[ LT ^{-1}\right]}{[ T ]}=\left[ LT ^{-2}\right]$
Dimensions of $c=[t]=[ T ]$
(we can add quantities of same dimensions only).
${\left[\frac{b}{t+c}\right]=[v]=\left[ LT ^{-1}\right]} $
${[b]=\left[L T^{-1}\right][T]=[L]}$