Question

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

• A. a = L², b = T, c = LT²
• B. a = LT², b = LT, c = L
• C. a = LT^-2, b = L, c = T
• D. a = L, b = LT, c = T²

Answer 1

The correct option is C a = LT^-2, b = L, c = T

From the principle of dimensional homogeneity $\left[v\right]=\left[\alpha t\right]\Rightarrow \left[\alpha \right]=\left[L{T}^{-2}\right]$.
Similarly,$\left[b\right]=\left[L\right]and\left[c\right]=\left[T\right]$