Newton's Law of Gravitation: Practice Problem & Solution

Short Solution (Best for NEET):

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:

The centripetal force is provided by the gravitational force: \(m \omega^2 R = \frac{k}{R^n} ⇒ \omega^2 \propto \frac{1}{R^{n+1}}\). Since \(T = \frac{2\pi}{\omega}\), we get \(T^2 \propto R^{n+1} ⇒ T \propto R^{\frac{n+1}{2}}\).