Question

The dimensional formula for universal gravitational constant is 

(A) [M^-2]

(B) [M^-1L³T²]

(C) [M^-1L³T²]

(D) [ML²T^-2]

Answer 1

Correct option is (B) [M^-1L³T²]

According to the Newton's law of gravitation, the force attraction between two objects of mass m₁ and m₂ can be given as \(F = \frac{Gm_1m_2}{r^2}\), where G is the universal gravitational constant and r is the distance between the objects.

\(\therefore G = \frac{F \times r^2}{m_1 \times m_2}\)

Now, on putting the dimensional formula of F, r, m₁ and m₂ in the given expression, we can get the dimensional formula for G as 

\([G] = \frac{[F] \times [r^2]}{[m_1]\times [m_2]}\)

\(= \frac{[MLT^{-2}]\times [L^2]}{[M]\times [M]}\)

\(= [M^{-1}L^3T^{-2}]\)