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NTA Abhyas JEE Main2020PhysicsGravitationPractice

A cord of length h = 64 m is used to connect an astronaut ( m = 100 kg ) to a spaceship ( M ≫ m ) which is orbiting near the earth's surface as shown in the figure. Assuming that the spaceship and the astronaut fall on a straight line from the earth's centre, then the tension in the cord is close to [ R = 6400 km ]

Options

  1. A3 × 1 0 - 2 N
  2. B2 × 1 0 - 2 N
  3. C4 × 1 0 - 2 N
  4. D5 × 1 0 -2 N

Correct answer

A. 3 × 1 0 - 2 N

Step-by-step solution

According to given problem, the mass of satellite M is much greater than that of astronaut m . So the centre of mass of the system will be close to satellite and as the satellite is orbiting close to the surface of earth, the equation of motion of the system ( S + A ) will be- GM e ⁡ M ⁡ + m ⁡ R ⁡ 2 = M ⁡ + m ⁡ R ⁡ ω 2 i.e., R ⁡ ω 2 = GM e ⁡ R ⁡ 2 = g … i And the equation of motion of the astronaut will be GM e ⁡ m ⁡ r ⁡ 2

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