Q. The velocity $v$ (in $cm/sec$) of a particle is given in terms of time $t$(in $\sec$) by the relation $v = at + \frac{b}{t + c}$ ; 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) $a = L,\ b = LT,\ c = T^{2}$
Explanation
From the principle of dimensional homogenity $\lbrack v\rbrack = \lbrack at\rbrack \Rightarrow \lbrack a\rbrack = \lbrack LT^{- 2}\rbrack$. Similarly $\lbrack b\rbrack = \lbrack L\rbrack$ and $\lbrack c\rbrack = \lbrack T\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.