JEE PYQ: Gravitation Question 39
Question 39 - 2019 (10 Apr Shift 2)
A spaceship orbits around a planet at a height of 20 km from its surface. Assuming that only gravitational field of the planet acts on the spaceship, what will be the number of complete revolutions made by the spaceship in 24 hours around the planet?
[Given: Mass of Planet $= 8 \times 10^{22}$ kg, Radius of planet $= 2 \times 10^6$ m, Gravitational constant $G = 6.67 \times 10^{-11}$ Nm$^2$ kg$^{-2}$]
(1) 9
(2) 17
(3) 13
(4) 11
Show Answer
Answer: (4)
Solution
$r = (2 \times 10^6 + 20 \times 10^3) \approx 2.02 \times 10^6$ m. $T = 2\pi\sqrt{\frac{r^3}{GM}} \approx 7812$ s $\approx 2.17$ hr. Number of revolutions in 24 hr $= 24/2.17 \approx 11$.
BETA
