Question

The physical quantity which has dimensional formula as that of $\frac{\text{Energy}}{\text{Mass x length}}$ is:

• A. force
• B. power
• C. pressure
• D. acceleration

Answer 1

Answer: (D)

$\frac{Energy}{Mass\times length}=\frac{[M{L}^2{T}^{-2}]}{[M][L]}=[L{T}^{-2}]$ Force (F) = Mass(m) $\times$ acceleration $\therefore$ $[F]=[M][L{T}^{-1}]$ $=[ML{T}^{-1}]$ Power (P) = Force (F) $\times$ velocity (v) $\therefore$ $[P]=[ML{T}^{-2}][L{T}^{-1}]$ $=[M{L}^2{T}^{-3}]$ Pressure (p) $\text{(P) = }\frac{\text{Force (F)}}{\text{Area (A)}}$ $\therefore$ $[p]=\frac{[ML{T}^{-2}]}{[L^2]}=[M{L}^{-1}{T}^{-2}]$ Acceleration $\text{(a) =}\frac{\text{Forece }[\text{ F }]}{\text{Mass(m)}}$ $\Rightarrow$ $[a]=\frac{[ML{T}^{-2}]}{[m]}=[L{T}^{-2}]$ So, choice is correct.