Question

Find the dimensions of the following quantities:
(i) the surfaces tension S, (ii) the coefficient of viscosity $\eta$.

Some equations involving these quantities are

$S=\frac{\rho grh}{2}$ and $F=-\eta A\frac{v_2-v_1}{x_2-x_1}$

Where the symbol have their usual meanings.

$\rho$ is density g is acceleration r, h and x are length

F is force, A is area.

• A. $\left[S\right]=M{T}^{-2},\left[\eta \right]=M{L}^{-1}{T}^{-1}$
• B. $\left[S\right]=M{T}^{-2},\left[\eta \right]=M^{-2}LT$
• C. $\left[S\right]=MT,\left[\eta \right]=M{L}^{-1}{T}^{-1}$
• D. none of these

Answer 1

The correct option is A

$\left[S\right]=M{T}^{-2},\left[\eta \right]=M{L}^{-1}{T}^{-1}$

(i) $S=\frac{\rho grh}{2}$

or $\left[S\right]=\left[\rho \right]\left[g\right]L^2=\frac{M}{L^3}.\frac{L}{T^2}.L^2=M{T}^{-2}$

(ii) $F=-\eta A\frac{v_2-v_1}{x_2-x_1}$

or, $ML{T}^{-2}=\left[\eta \right]L^2\frac{\frac{L}{T}}{L}=\left[\eta \right]\frac{L^2}{T}$

or, $\left[\eta \right]=M{L}^{-1}{T}^{-1}$