The velocity of a freely falling body changes as gphq where . . .

Question : 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

a) 1/2 and 1

b) both are 1/2

c) 1 and 1/2 

d) both are 1

Doubt by Ananya

Solution : 

v = g^ph^q

where
v = velocity

g = acceleration due to gravity 

h = height

Using the principle of Homogeneity 
[M⁰L¹T^-1] = [M⁰L¹T^-2]p[M⁰L¹]q
[M⁰L¹T^-1] = [M⁰L^p+qT^-2p]

Comparing the power of L and T both the sides.
-1=-2p
1=2p
p=1/2

Also, 
1=p+q
1=1/2+q
1-1/2=q
1/2=q
q=1/2

∴ p=1/2 and q=1/2

Hence, b) is the correct answer.