Question

Check the corectnes of relation v =underoot 2GM/R

Answer 1

Correctness of relation v =underoot 2GM/R :

Checking by dimension formula method.

We know that,

• Dimension formula of v = [ LT^-1]

• Dimension formula of G = [M^-1L^3T^-2]

• Dimension formula of M = [M]

• Dimension formula of R = [L]

• Dimension of √2GM/R

= { [M^-1L^3T^-2]×[M]/[L] }^1/2

= { [L^2T^-2] }^1/2

= [ LT^-1 ]

= Dimension formula of v

• Hence, it is proved that the above relation is correct.