Question

Prove that if the Earth attracts two bodies placed at the same distance from the centre of Earth with equal force; then their masses will be the same.​

Answer 1

Answer:

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Answer 2

We know that gravitational force between any two objects is:

$G\frac{m_1m_2}{d^2}$

Where G is Universal gravitational constant, m₁ and m₂ are their masses respectively and d is the distance between them.

Let distance between Earth and Body1 =Distance between Earth and Body2

= d

Let mass of earth be m, mass of Body1 be m₁ and mass of Body2 be m₂

Given, Earth attracts the two bodies with equal force.

$G\frac{mm_1}{d^2} = G\frac{mm_2}{d^2} \\\frac{mm_1}{d^2} = \frac{mm_2}{d^2}\\mm_1 = mm_2\\m_1 = m_2$

Hence proved.

∴ The masses of the two bodies are same.

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