Question

Two objects of mass m₁ and m₂ are separated by a distance r. The ratio of the magnitudes of gravitational force between them and the gravitational potential energy of any one object at that distance is
1. 1 : r
2. r² : 1
3. 1 : r²
4. r : 1

Answer 1

Correct Answer - Option 1 : 1 : r

The correct answer is option 1) i.e. 1 : r

CONCEPT:

• Law of Universal Gravitation: It states that all objects attract each other with a force that is proportional to the masses of two objects and inversely proportional to the square of the distance that separates their centres.

It is given mathematically as follows:

\(F = \frac{Gm_1m_2}{R^2}\)

Where m1 and m2 are the mass of two objects, G is the gravitational constant and R is the distance between their centres.

• Gravitational Potential Energy: It is the energy possessed by a body at a certain point when work is done by the force of gravity in bringing the object from infinity to that point.

The gravitational potential energy of mass m at a distance r from the gravity due to mass M is given by:

U = \(-\frac{GMm}{r}\)

Where G is the gravitational constant.

CALCULATION:

The gravitational force between m₁ and m₂, \(F = \frac{Gm_1m_2}{r^2}\)

The gravitational potential energy of mass m₁ at a distance r, U = \(-\frac{Gm_1m_2}{r}\)

Ratio of magnitudes = \(\frac{F}{U}\) = \(\frac{\frac{Gm_1m_2}{r^2}}{\frac{Gm_1m_2}{r}}\) = \(\frac{1}{r}\)