Question

An object is falling freely under the gravitational force its velocity after travelling a distance h is V if we depends upon gravitational acceleration G and distance prove it dimensional analysis that V = k andar root 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...