• # question_answer The velocity v (in cm/s) of a particle is given in terms of time? (in second) by the equation$v=at+\frac{b}{t+c}$ The dimensions of a, b and c are A) a b c $[{{L}^{2}}]$ $[T]$ $[L{{T}^{2}}]$ B) a b c $[L{{T}^{2}}]$ $[LT]$ $[T]$ C) a b c $[L{{T}^{-2}}]$ $[L]$ $[T]$ D) a b c $[L]$ $[LT]$ $[{{T}^{2}}]$

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