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MHT CET202410 May 2024Evening ShiftPhysicsGravitationActual

A body starts from rest from a distance R ₀ from the centre of the earth. The velocity acquired by the body when it reaches the surface of the earth will be ( R = radius of earth, M = mass of earth )

Options

  1. A2 GM ( 1 R - 1 R ₀ )
  2. B2 GM ( 1 R - 1 R ₀ )
  3. CGM ( 1 R - 1 R ₀ )
  4. D2 GM ( 1 R - 1 R ₀ )

Correct answer

B. 2 GM ( 1 R - 1 R ₀ )

Step-by-step solution

According to law of conservation of energy, 1 2 m v^2=- GMm R ₀ - ( GMm R )= GMm ( 1 R - 1 R ₀ ) v ^2=2 GM ( 1 R - 1 R ₀ ) The velocity acquired by the body when it reaches the surface of earth is: v = 2 GM ( 1 R - 1 R ₀ ) Amongst the given options, only option (B) dimensionally equates to velocity.

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