Question

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

• A. $1,\frac{1}{2}$
• B. $M^{0}L^{2}T^{- 2}$
• C. $\frac{1}{2},1$
• D. $1,1$

Answer 1

Answer: (B)

$M^{0}L^{2}T^{- 2}$

Answer 2

$v \propto g^{p}h^{q}$ (given)

By substituting the dimension of each quantity and comparing the powers in both sides we get

$\lbrack LT^{- 1}\rbrack = \lbrack LT^{- 2}\rbrack^{p}\lbrack L\rbrack^{q}$

$\Rightarrow$ $p + q = 1, - 2p = - 1,\therefore p = \frac{1}{2},q = \frac{1}{2}$