Answer to Question #200420 in Math for Raghav

Question #200420

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.


1
Expert's answer
2021-06-01T08:50:31-0400

Dimension of V is msec.\dfrac{m}{sec}.


Dimension of g is msec2.\dfrac{m}{sec^2}.


Dimension of h is m.m.


Thus, dimension of gh\sqrt{gh} is 

mmsec2=msec=dimension of V.\sqrt{m\cdot \frac{m}{sec^2}}=\dfrac{m}{sec}=\text{dimension of V.}

 

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

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