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

`x prop g^(p)h6^(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)`
`rArr p + q = 1, 2p = -1, :. P = (1)/(2), q= (1)/(2)`