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

Options

A. `1`,`(1)/(2)`
B. `(1)/(2)`,`(1)/(2)`
C. `(1)/(2)`,`1`
D. 1,1

Answer

B

Explanation

`upsilonpropg^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`
`implies=p+q=1`,`-2p=-1`,because `p=(1)/(2)`,`q=(1)/(2)`