Concepts Of Physics MCQ Edition [Volume 1]PhysicsGravitation
A 1000 ext kg satellite is intended to orbit the earth at an altitude of 2000 ext km above the earth's surface. Determine its time period. The mass of the earth is 6 imes 10²⁴ ext kg .
Options
- A1.41 ext hours
- B2.12 ext hours
- C3.18 ext hours
- D4.24 ext hours
Correct answer
B. 2.12 ext hours
Step-by-step solution
Radius of earth, R = 6400 km Altitude of the satellite, h = 2000 km Orbital radius, r = R + h = 6400 + 2000 = 8400 km = 8.4 10^6 m Mass of earth, M = 6 10²⁴ kg The time period of the satellite is given by: T = 2 r^3 GM Substituting the values ( G = 6.67 10⁻¹¹ N m ^2 kg ⁻² ): T = 2 (8.4 10^6)^3 6.67 10⁻¹¹ 6 10²⁴ T = 2 592.7 10¹⁸ 40.02 10¹³ T = 2 1.481 10^6 T = 2 3.1416 1217 T 7646 s Converting to hours: T = 7646 3600 hours 2.12 hours