Question

The physical quantity which has the dimensional formula $\left[M^{}{T}^{-3}\right]$ is:

• A. Surface tension
• B. Density
• C. Solar constant
• D. Compressibility

Answer 1

The correct option is C Solar constant

Surface tension, $S=\frac{F}{l}$

Dimensional formula of force, $F=\left[ML{T}^{-2}\right]$

$\therefore$ Dimensional formula for surface tension, $S=\frac{ML{T}^{-2}}{\left[L\right]}=\left[M{T}^{-2}\right]$

Dimensional formula for density, $\rho =\frac{M}{V}=\frac{M}{L^3}=\left[M{L}^{-3}\right]$

Solar constant $=\frac{\sigma R_s^2{T}_s^4}{R_{se}^2}$ where all symbols have their usual meaning

Dimension of Stefan's constant, $\sigma =\left[M{T}^{-3}{K}^{-4}\right]$

$\therefore$ Dimensional formula for solar constant $=\frac{\left[M{T}^{-3}{K}^{-4}\right]\times L^2\times K^4}{L^2}=\left[M{T}^{-3}\right]$

Compressibility, $k=-\frac{\Delta V}{V}\frac{1}{\Delta P}$

$\therefore$ Dimensional formula for compressibility, $k=\frac{\left[L^3\right]}{\left[L^3\right]\times \left[M{L}^{-1}{T}^{-2}\right]}=\left[M^{-1}L{T}^2\right]$