MCQ
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$1,\frac{1}{2}$
- ✓$\frac{1}{2},\frac{1}{2}$
- C$\frac{1}{2},\,1$
- D$1,\,1$
✓
Answer
Correct option: B.
$\frac{1}{2},\frac{1}{2}$
b
(b) $v \propto {g^p}{h^q}$ (given)
(b) $v \propto {g^p}{h^q}$ (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 $ $p + q = 1,\,\, - 2p = - 1,\,$
$\therefore \,\,p = \frac{1}{2},\,q = \frac{1}{2}$
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