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Concepts Of Physics MCQ Edition [Volume 1]PhysicsGravitation

A satellite of Mars travelling in an orbit of radius 9.4 10^3 km requires 27540 s to complete one revolution. Calculate the mass of Mars.

Options

  1. A6.5 10²³ kg
  2. B1.3 10²⁴ kg
  3. C6.5 10²⁴ kg
  4. D3.2 10²³ kg

Correct answer

A. 6.5 10²³ kg

Step-by-step solution

The time period of a satellite revolving around a planet is given by: T = 2 r^3 GM Squaring both sides, we get: T^2 = 4 ^2 r^3 GM Rearranging for the mass of Mars M : M = 4 ^2 r^3 G T^2 Given: r = 9.4 10^3 km = 9.4 10^6 m T = 27540 s G = 6.67 10⁻¹¹ N m ^2 kg ⁻² Substituting the values: M = 4 (3.14)^2 (9.4 10^6)^3 6.67 10⁻¹¹ (27540)^2 M = 4 9.86 830.58 10¹⁸ 6.67 10⁻¹¹ 7.585 10^8 M = 32758 10¹⁸ 50.59 10⁻³ M 6.48 10²³ kg Rounding off to one decimal place, we get: M 6.5 10²³ kg

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