Gravitational force between two doubled masses and distance – Rankers Physics

Newton's Law of Gravitation: Practice Problem & Solution

The gravitational force of attraction between two bodies is \(F\) newtons. If the mass of each body and the distance between them are doubled, then the gravitational force between them in newton is
\(16 F\)
\(F/16\)
\(F/4\)
\(F\)

Solution Explained:

To solve this problem, we apply the core principles of Newton's Law of Gravitation. Understanding the underlying formula is key to arriving at the correct answer below:

Formula of gravitational force is \(F = \frac{G m_1 m_2}{r^2}\). If masses and distance are doubled: \(F' = \frac{G(2m_1)(2m_2)}{(2r)^2} = \frac{4 G m_1 m_2}{4 r^2} = F\). Thus, the force remains unchanged.

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