Question

Using the principle of homogeneity of dimensions, find which of the following relation is correct? [T is the time period, a is the radius of the orbit and M is the mass of the sun.]

(A) T² = \(\frac{4\pi^2a^3}{G}\)

(B) T² = \(\frac{4\pi^2a^3}{GM}\) 

(C) T² = 4π²a³

(D) T² = \(\frac{4\pi^2a^3}{GM^2}\) 

Answer 1

Answer is  (B) T² = \(\frac{4\pi^2a^3}{GM}\) 

Comparing powers of M, L and T 

y - z = 0, 

x - 3y = 0 and 2y = 2 

∴ y = 1

Substituting value of y, 

z = 1, x = 3

Thus, T² =  \(\frac{4\pi^2a^3}{GM}\)