Obtain the dimensional formula for universal gas constant. 

According to ideal gas equation, i.e. pV = nRT, where n is the number of moles of gases.
Universal gas constant, $\mathrm{R}=\frac{\left(\mathrm{p}\right)\left(\mathrm{V}\right)}{\left(\mathrm{n}\right)\left(\mathrm{T}\right)}$
Dimensional formula of R = $\frac{\left[{\mathrm{ML}}^{-1}{\mathrm{T}}^{-2}\right]\left[{\mathrm{L}}^3\right]}{\left[\mathrm{mol}\right]\left[\mathrm{K}\right]}$
= [ML²T^-2 mol^-1K^-1]