Inverse Cube Law of Gravitation – Rankers Physics

Planet and Satellite: Practice Problem & Solution

Assertion (A): If the law of gravitation, instead of being inverse square law then planets will still have elliptical orbits. Reason (R): In that case also, \( T^2 \propto r^3 \) (symbols having usual meanings)  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Planet and Satellite. Understanding the underlying formula is key to arriving at the correct answer below:

Assertion (A) is false. Only an inverse-square force leads to stable, closed elliptical orbits. An inverse cube law would lead to unstable orbits. Reason (R) is also false. Kepler's third law, \( T^2 propto r^3 \), is a direct consequence of the inverse-square law. If the law changes, this relation no longer holds. Therefore, both (A) and (R) are false.

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