Question

A spaceship orbits around a planet at a height of 20 km from its surface. Assuming that only gravitational field of the plant acts on the spaceship. What will be the number of complete revolutions made by the spaceship in 24 hours around the plane?
[Given: Mass of plane = 8 × 10²² kg, Radius of planet = 2 × 10⁶ m, Gravitational constant G = 6.67 × 10⁻¹¹ Mn²/kg²]
(A) 9 (B) 11
(C) 13 (D) 17

Answer 1

Explanation:

Given A spaceship orbits around a planet at a height of 20 km from its surface. Assuming that only gravitational field of the plant acts on the spaceship. What will be the number of complete revolutions made by the spaceship in 24 hours around the plane?

• So there is a planet and a space ship around it at a height of 20 km. So there is a force outside and inside. The force that is inside is gravitational and the one that is outside is centripetal force.
• So the balanced condition of the force will be
•                                             So mv^2 / r
•               Now radius = 2 x 10^6 m + 0.02 m
•                                     = 2.02 x 10^6 m
•                   So mv^2 / r = GMm / r^2
•                                v = √GM / r
•                                   = √6.67 x 10^-11 x 8 x 10^22 / 2.02 x 10^6
•                                 v = 1.625 x 10^3 m/s
• now we need to find the number of revolutions in 24 hours.
•             So time period `T = 2π r / v
•                             Now nT = 24 x 60 x 60
•                               So n(2π r / v) = 24 x 3600
•        So n  x 2 x 3.14 x 2.02 x 10^6 / 1.625 x 10^3 = 24 x 3600
•                       Or n = 140400000 / 12685600
•                       Or n = 11
• So number of spaceship revolving around the planet is 11

Reference link will be

https://brainly.in/question/1896830