Question

An object is falling freely under the gravitational force. It's velocity after traveling 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:

k = √2

Explanation:

An object is falling freely under the gravitational force. It's velocity after traveling 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

Using V² - U² = 2aS

U = 0   Falling freely

V = v

a = g

S = h

=> v² - 0 = 2gh

=> v = √2gh

=> v = √2 √gh

comparing with

v = k√gh

k = √2

Answer 2

Answer:

k = √2

Explanation:

An object is falling freely under the gravitational force. It's velocity after traveling 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

Using V² - U² = 2aS

U = 0   Falling freely

V = v

a = g

S = h

=> v² - 0 = 2gh

=> v = √2gh

=> v = √2 √gh

comparing with

v = k√gh

k = √2