JEE PYQ: Gravitation Question 27
Question 27 - 2020 (06 Sep Shift 1)
A satellite is in an elliptical orbit around a planet P. It is observed that the velocity of the satellite when it is farthest from the planet is 6 times less than that when it is closest to the planet. The ratio of distances between the satellite and the planet at closest and farthest points is:
(1) 1 : 6
(2) 1 : 3
(3) 1 : 2
(4) 3 : 4
Show Answer
Answer: (1)
Solution
By angular momentum conservation: $r_{\min}v_{\max} = r_{\max}v_{\min}$. Given $v_{\max} = 6v_{\min}$: $\frac{r_{\min}}{r_{\max}} = \frac{v_{\min}}{v_{\max}} = \frac{1}{6}$.
BETA
