Question

State and explain Newton’s Law of gravitation. Hence define universal gravitational constant and find the dimensional formula for it.

Answer 1

The gravitational force of attraction between two bodies is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. If two masses m₁ and m₂ are separated by a distance r then F ∝ \(\frac {m_{m2}}{r2}\) Or \(F =G\frac {m_1m_2}{r^2}\) Where G is the proportionality constant known as universal gravitational constant.

From the above equation, G = \(\frac {Fr^2}{m_1m_2}\)

If m₁ = m₂ = 1 and r = 1 then G = \(\frac {F(r^2)}{m_1m_2}\)

Gravitational constant is defined as the gravitational force attraction between two bodies of unit masses separated by unit distance. Dimensional formula for [G] = [M^-1 L³ T^-2 ].