The velocity of a freely falling body changes as $$g^ph^q$$ where g is acceleration due to gravity and h is the height. The values of p and q are
C
$$\dfrac{1}{2},\dfrac{1}{2}$$
Correct option is B. $$\dfrac{1}{2},\dfrac{1}{2}$$
$$ v \propto g^ph^q$$ (given)
By substituting the dimension of each quantity and comparing the powers in both sides
we get $$[LT^{-1}]=[LT^{-2}]^p[L]^q$$
$$\Rightarrow p+q=1,-2p=-1$$
$$ \therefore p=\dfrac{1}{2},q=\dfrac{1}{2}$$