Q 11-01-027NEETEAMCET 2011 (Medical)Medium
The velocity $v$ (in cm/s) of a particle is given in terms of time $t$ (in s) by the equation
$$v = at + \frac{b}{t + c}$$
The dimensions of $a$, $b$ and $c$ are
Answer: (C) $[LT^{-2}],\ [L],\ [T]$
Only like quantities can be added, so $c$ has the dimensions of time: $[c] = [T]$.
$at$ is a velocity: $[a] = \dfrac{[LT^{-1}]}{[T]} = [LT^{-2}]$
$\dfrac{b}{t+c}$ is a velocity: $[b] = [LT^{-1}][T] = [L]$
Solution by Sreeraj P, M.Sc Physics