Answer to Question #200420 in Math for Raghav

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 $\dfrac{m}{sec}.$

Dimension of g is $\dfrac{m}{sec^2}.$

Dimension of h is $m.$

Thus, dimension of $\sqrt{gh}$ is 

$$\sqrt{m\cdot \frac{m}{sec^2}}=\dfrac{m}{sec}=\text{dimension of V.}$$

 

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