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)

a -$[LT^{-2}]$ b- $[L]$ c- $[T]$

Answer 2

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