Question

What is the dimensional analysis of P=3g/4rG

Answer 1

Answer:

We have to find the dimensional analysis of p = 3g/4rG. The breakdown of the above formula is as follow:

Explanation:

In the formula p is density, g is the acceleration that exists due to the presence of gravity, r represents the radius while G is the representation of universal gravitational constant.

To analyse the dimensions of the formula:

1. Dimension of  density (p) is = [ML^-3]
2. Dimension of acceleration (g) is = [LT^-2]
3. Dimension of radius (r) is = [L]
4. Dimension of gravitational constant (G) is = [M^-1L^3T^-2]

To further prove this point,

Dimensions of LHS = Dimensions of RHS  should be the case if formula is correct.

LHS is   = [ML-3]

while

RHS is  = [LT-2]  / { [L] . [M-1L3T-2] }   = [ML-3]

Hence the formula is correct.