Physics - Unit & Dimension Question with Solution | TestHub

Viscous force is given by, $F=\eta A\frac{dv}{dy}$.

Hence, $\left[{\mathrm{MLT}}^{-2}\right]=\eta \left[{\mathrm{L}}^2\right]\left[{\mathrm{T}}^{-1}\right]$

$\Rightarrow \eta =\left[{\mathrm{ML}}^{-1}{\mathrm{T}}^{-1}\right]$

Surface tension is given by, $ST=\frac{F}{\ell }$.

Hence, dimension will be $=\frac{\left[{\mathrm{MLT}}^{-2}\right]}{\left[\mathrm{L}\right]}=\left[{\mathrm{ML}}^0{\mathrm{T}}^{-2}\right]$

Angular momentum, $L=mvr=\left[{\mathrm{ML}}^2{\mathrm{T}}^{-1}\right]$

Rotational kinetic energy, $K.E=\frac{1}{2}I{\omega }^2=\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right]$