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MHT CET202314 May 2023Evening ShiftPhysicsGravitationActual

A body (mass m ) starts its motion from rest from a point distant R₀ (R₀>R ) from the centre of the earth. The velocity acquired by the body when it reaches the surface of earth will be ( G = universal constant of gravitation, M = mass of earth, R = radius of earth)

Options

  1. A2 GM ( 1 R - 1 R ₀ )
  2. B[2 GM ( 1 R - 1 R ₀ ) ]^ 1 2
  3. CGM ( 1 R - 1 R ₀ )
  4. D2 GM [ ( 1 R - 1 R ₀ ) ]^ 1 2

Correct answer

B. [2 GM ( 1 R - 1 R ₀ ) ]^ 1 2

Step-by-step solution

According to law of conservation of energy, aligned & 1 2 mv ^2=- GMm R ₀ - ( GMm R )= GMm ( 1 R - 1 R ₀ ) & v ^2=2 GM ( 1 R - 1 R ₀ ) aligned The velocity acquired by the body when it reaches the surface of earth is: V = [2 GM ( 1 R - 1 R ₀ ) ]^ 1 2

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