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Q.
The velocity of a freely falling body changes as $g^{p}h^{q}$ where g is acceleration due to gravity and h is the height. The values of p and q are
Physical World, Units and Measurements
Solution:
$v \propto g^{p}h^{q}$ (given)
By substituting the dimension of each quantity and comparing the powers in both sides we get
$\left[LT^{-1}\right]=\left[LT^{-2}\right]^{p}\left[L\right]^{q}$
$\Rightarrow p+q=1, -2p=-1$,
$\therefore p=\frac{1}{2},q=\frac{1}{2}$