The velocity of a freely falling body changes as gphq where g is acceleration due to gravity and h is the height. The values of p and q are

Question

The velocity of a freely falling body changes as gphq where g is acceleration due to gravity and h is the height. The values of p and q are (A) 1,(1/2) (B) (1/2),(1/2) (C) (1/2),1 (D) 1,1

Tardigrade Admin · Accepted Answer

v propto gphq (given) By substituting the dimension of each quantity and comparing the powers in both sides we get [LT-1]=[LT-2]p[L]q ⇒ p+q=1, -2p=-1, ∴ p=(1/2),q=(1/2)

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

$1, \frac{1}{2}$

$\frac{1}{2}, \frac{1}{2}$

$\frac{1}{2}, 1$

$1, 1$

$v \propto g^{p} h^{q}$ (given)
By substituting the dimension of each quantity and comparing the powers in both sides we get
$[L T^{- 1}] = [L T^{- 2}]^{p} [L]^{q}$
$\Rightarrow p + q = 1, - 2 p = - 1$ ,
$∴ p = \frac{1}{2}, q = \frac{1}{2}$

Q. The velocity of a freely falling body changes as gphq where g is acceleration due to gravity and h is the height. The values of p and q are

1,21​

21​,21​

21​,1

1,1