Suppose the law of gravitational attraction suddenly changes and becomes an inverse-cube law, i.e. F 1/r^3, but still remains a central force. Then [UPSEAT 2002]

JEE Main Physics question

Suppose the law of gravitational attraction suddenly changes and becomes an inverse-cube law, i.e. , but still remains a central force. Then [UPSEAT 2002]

(A)Kepler's law of areas still holdsCorrect
(B)Kepler's law of period still holds
(C)Kepler's law of areas and period both still hold
(D)Neither the law of areas nor the law of period still holds

Answer: (A)

Solution

For any central force — one directed along the line joining the two bodies, whatever power of it depends on — the torque about the force centre is zero, so angular momentum, and hence the areal velocity , remains constant. Kepler's law of areas is thus a general consequence of centrality alone and

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Question ID VK-154737