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
Solution:
Assertion (A) is false. According to Bertrand's Theorem, 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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