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The velocity of a freely falling body under gravity varies as g^p h^q where g is the acceleration due to gravity and his the height through which the body is falling . Find the values of p and q using dimensional analysis.

The velocity of a freely falling body under gravity varies as g^p h^q where g is the acceleration due to gravity and his the height through which the body is falling . Find the values of p and q using dimensional analysis.

Grade:11

2 Answers

Khimraj
3007 Points
7 years ago
As the unit of velocity is m/s and g is m/s² and h is m so the value of P and Q are 1/2 as √(m/s²)(m) = m/s.Hope it clears. If u have doubts then please clearify. And if u like my answer then please approve answer
Jayati Majumdar
13 Points
4 years ago
answer : p = 1/2 and q = 1/2
explanation : A body is falling freely under gravity. so, initial velocity of body will be zero. let v is the velocity of body when it falls h from the initial position.
using formula, v² = u² + 2as
here, a = -g , u = 0 and s = -h
then, v² = 0 + 2(-g)(-h)
or, v² = 2gh
or, v = √(2gh) = √2(gh)½
here it is clear that velocity of a body has fallen freely under gravity varies as (gh)½.
on comparing with g^ph^q ,
we get p = 1/2 and q = 1/2
 
 

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