Question

An object is falling freely under gravitational force its velocity after travelling h is v if v depends upon gravitational acceleration g and distance d then prove with the help of dimensional analysis V==√gh

Answer 1

total work on the object = force * distance = mgh

change in kinetic energy = work done = 0.5mv(final)^2 - 0.5mv(initial)^2 = mgh.

Assuming initial velocity is zero:

0.5mv(final)^2 = mgh --> v(final) = sqrt(2gh).