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 gh where k is a constant.​

Answer 1

Answer:

v=k

gh

Dimensional formula v=[LT

−1

].

Dimension v=

gh

=

[g][h]

=

[LT

−1

][L]

=

[LT

−1

]

2

=[LT

−1

]

∴[v]=[k][

gh

]

[k]=

[

gh

]

[v]

=

LT

−1

LT

−1

[0]

k is dimensionless.

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