If the radius of the Earth is halved and the masses of both interacting objects are tripled, while keeping the distance between them unchanged, how will the gravitational force between them change?

📘 Explanation

According to the Law of Gravitation given by Isaac Newton:

$F = \dfrac{G m_1 m_2}{r^2}$

Where:

• $F$ = gravitational force

• $G$ = gravitational constant

• $m_1, m_2$ = masses

• $r$ = distance between them

Step 1: Effect of Tripling Both Masses

If both masses are tripled:

New masses = $3m_1$ and $3m_2$

New force:

$F' = \dfrac{G (3m_1)(3m_2)}{r^2}$

$F' = \dfrac{9G m_1 m_2}{r^2}$

So, force becomes 9 times.

Step 2: Effect of Halving Earth's Radius

Since the question clearly states that the distance between them remains unchanged, the change in Earth's radius does not affect the force.

Gravitational force depends on:

• Masses

• Distance between centers

 Therefore, the gravitational force increases 9 times.

📗 व्याख्या

Isaac Newton के गुरुत्वाकर्षण नियम के अनुसार:

$F = \dfrac{G m_1 m_2}{r^2}$

यदि दोनों द्रव्यमान को 3 गुना कर दिया जाए:

$F' = \dfrac{G (3m_1)(3m_2)}{r^2}$

$F' = 9F$

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