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JEE MainPhysicsGravitation

A body of mass m is raised from the surface of the earth to a height h . If the work done against gravity is 4 5 mgR , where g is the acceleration due to gravity on the surface of the earth and R is the radius of the earth, the value of h is:

Options

  1. A4 5 R
  2. B4R
  3. C5R
  4. DR

Correct answer

B. 4R

Step-by-step solution

The change in gravitational potential energy when a body is raised to a height h from the surface of the earth is given by: U = mgh 1 + h R According to the problem, the work done against gravity is equal to the change in potential energy: U = 4 5 mgR Equating the two expressions: mgh 1 + h R = 4 5 mgR h 1 + h R = 4 5 R 5h = 4R (1 + h R ) 5h = 4R + 4h h = 4R Answer: 4R

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