Question

The velocity v (in cm / sec) 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 = $L^2$, b = T, c = $L{T}^2$
• B. a = $L{T}^2$, b = LT, c = L
• C. a = $L{T}^{-2}$, b = L, c = T
• D. a = L, b = LT, c = $T^2$

Answer 1

The correct option is C a = $L{T}^{-2}$, b = L, c = T

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