A particle of mass $m$ is moving in an elliptical orbit about a bigger mass M, which is at one of its focus. $v_{A}, v_{B}, v_{C}$ and $v_{D}$ are the velocities of the particle at the points A,B,C and D and $r_{A}, r_{B}, r_{C}$ and $r_{D}$ are the distances of the points A, B, C and D from the bigger mass respectively. Which of the following relation is/are incorrect

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$\frac{GMm}{r_{B}^{2}} = \frac{{mv}_{B}^{2}}{r_{B}}$

$\frac{GMm}{r_{D}^{2}} = \frac{{mv}_{D}^{2}}{r_{D}}$

$\frac{GMm}{r_{C}^{2}} = \frac{{mv}_{C}^{2}}{r_{C}}$

$\frac{GMm}{r_{A}^{2}} = \frac{{mv}_{A}^{2}}{r_{A}}$

answer is A, B, C, D.

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Detailed Solution

In centripetal force $\frac{{mV}^{2}}{r}$ , r is the radius of curvature. It is not the distance of the point from bigger mass. Necessary centripetal force is provided by gravitational force. Hence all are incorrect.

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