Answer to Question #163062 in Math for Ajay

Question

A body is falling free in a vacuum. The fall is necessarily related to the gravitational 

acceleration g and the height h from which the body is dropped. Use dimensional 

analysis to show that the velocity V of the falling body satisfies the relation 

V / √gh = constant

Answer 1

Dimension of V is $\frac{m}{sec}.$

Dimension of g is $\frac{m}{sec^2}.$

Dimension of h is $m.$

Thus, dimension of $\sqrt{gh}$ is $\frac{m}{sec}=$ dimension of V.

Therefore, the relation $\frac{V}{\sqrt{gh}}=constant.$