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. $\frac{1}{2},\frac{1}{2}$
• C. $\frac{1}{2},1$
• D. $1,1$

Answer 1

The correct option is B $\frac{1}{2},\frac{1}{2}$

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

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

we get $\left[L{T}^{-1}\right]=\left[L{T}^{-2}{]}^p\right[L{]}^q$

$\Rightarrow p+q=1,-2p=-1$

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