Question

The dimension ML⁻¹T⁻² can correspond to
(a) moment of a force
(b) surface tension
(c) modulus of elasticity
(d) coefficient of viscosity

Answer 1

Correct option: (c)
​Dimension of modulus of elasticity: $\frac{{\displaystyle \raisebox{1ex}{$F$}\!\left/ \!\raisebox{-1ex}{$A$}\right.}}{{\displaystyle \raisebox{1ex}{$∆l$}\!\left/ \!\raisebox{-1ex}{$l$}\right.}}=\frac{\left[ML{T}^{-2}\right]}{L^2}=\left[M{L}^{-1}{T}^{-2}\right]$
Dimension of moment of force: ​$FL=\left[ML{T}^{-2}\right]\left[L\right]=\left[M{L}^2{T}^{-2}\right]$
Dimension of surface tension: ​$\frac{F}{{\displaystyle L}}=\frac{\left[ML{T}^{-2}\right]}{L}=\left[M{T}^{-2}\right]$
Dimension of coefficient of viscosity: ​$\frac{FL}{{\displaystyle Av}}=\frac{\left[ML{T}^{-2}\right]\left[L\right]}{\left[L^2\right]\left[L{T}^{-1}\right]}=\left[M{L}^{-1}{T}^{-1}\right]$