Question

Check the correctness of the following V^2=2GM/R^2

Answer 1

Answer:

you mean, we have to check is dimensionally correct or not . right ?

okay, first of all, we identify what is G , M, R and v .

G is gravitational constant.so, unit of G = Nm²/Kg²

and dimension of G = [M^-1L^3T^-2]

M is mass so, unit of M = kg

and dimension of M = [M]

R is radius so, unit of R = m

and dimension of R = [L]

v is velocity so, unit of v = m/s

and dimension of v = [LT^-1]

now, LHS = dimension of v = [LT^-1]

RHS = dimension of √{2GM/R}

= {dimension of G × dimension of M/dimension of R}½

= {[M^-1L^3T^-2][M]/[L]}½

= [LT^-1]

hence, LHS = RHS

so, formula is dimensionally correct.