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0.0.UUUUUix)xiv)An object is falling freely under thegravitational force. Its velocity aftertravelling a distance his v. If v dependsupon gravitational acceleration g anddistance, prove with dimensionalanalysis that v=kgh where k is aconstant.

Answer»

◆ 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)


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