Question

how to check the correctness of p=3g/4rG in dimensional analysis

Answer 1

given expression, $\rho=\frac{3g}{4rG}$

where $\rho$ is density , g is acceleration due to gravity , r is radius and G is universal gravitational constant.

• dimension of $\rho$ = [ML^-3]
• dimension of g = [LT^-2]
• dimension of r = [L]
• dimension of G = [M^-1L^3T^-2]

expression will be dimensionally correct,

dimension of $\rho$= dimension of {g/rG}

LHS = dimension of $\rho$ = [ML^-3]

RHS = dimension of {g/rG} = dimension of g/dimension of r × dimension of G

= [LT^-2]/[L][M^-1L^3T^-2]

= [ML^-3]

here, LHS = RHS

so, expression is dimensionally correct.

Answer 2

Answer:

Explanation:

we have

ρ = (3g / 4.r.G)

here,

the dimensions of LHS is

= [ML-3]

the dimensions of RHS will be

= [LT-2]  / { [L] . [M-1L3T-2] }

= [ML-3]

so,

as dimensions of LHS = dimensions of RHS

the above equation is dimensionally correct.