Question

An object is falling freely under the gravitational force.its velocity after travelling a distance h is v.If v depends upon gravitational acceleration g and distance, prove with dimensional analysis that
$v = k \sqrt{gh \: \:}$
where k is a constant. ​

Answer 1

Hey Dear,

◆ Answer -

v = k √(gh)

◆ Explaination -

For a object falling freely under gravity, let velocity be expressed as -

v = k.g^x.h^y

Substituting known dimensions of given quantities -

[v] = [g]^x [h]^y

[L1T-1] = [L1T-2]^x [L]^y

[L1T-1] = [L^(x+y) T^(-2x)]

Comparing indexes -

x + y = 1

-2x = -1

Solving these eqns,

x = 1/2

y = 1/2

Therefore, velocity of freely falling body would be -

v = k.g^½.h^½

v = k √(gh)

Hope this helps you...

Answer 2

Answer:

that's the answer

hope you help......