An equation is given as $$\left( {p + \frac{a}{{{V^2}}}} \right) = b\frac{\theta }{V},$$    where $$p =$$  pressure, $$V =$$  volume and $$\theta =$$  absolute temperature. If $$a$$ and $$b$$ are constants, then dimensions of $$a$$ will be

Solution :
From principle of homogeneity of dimensions. Dimensions of $$p =$$  dimensions of $$\frac{a}{{{V^2}}}$$
$$\eqalign{ & p = \frac{a}{{{V^2}}} \Rightarrow a = p{V^2} \cr & = \left[ {M{L^{ - 1}}{T^{ - 2}}} \right]{\left[ {{L^3}} \right]^2} \cr & = \left[ {M{L^5}{T^{ - 2}}} \right] \cr} $$