Question

The energy required to remove a body of mass m from earth’s surface is/are equal to:
(A) \[ - \dfrac{{G{m_1}{m_2}}}{r}\]
(B) mgR
(C) \[ - mgR\]
(D) None of these

Answer 1

Hint: For a body to be removed from the surface of the earth, the energy to be given to that object so that its total energy becomes zero. If the potential energy at the surface is \[P = \dfrac{{G{m_1}{m_2}}}{r}\] the kinetic energy should also be equal to that. So, for a body of mass m follows the same and the energy required is mgR.

Complete step-by-step solution
A body of m mass on which is placed on earth’s surface will have some potential energy and no kinetic energy. This potential energy is written as
 \[P = \dfrac{{G{m_1}{m_2}}}{r}\]
Planets being around the sun or electrons moving around the nucleus will have negative potential energy, because they are bound to the central entity. They require some energy to escape that loop or break that bond. This energy would be the required energy to remove a body of mass m from the earth’s surface.

Therefore, the correct answer is option B

Note The minimum velocity with which a body must be projected up so as to enable it to just overcome the gravitational pull, is called escape velocity. This velocity is independent of the mass and the direction of the projection of the body. It is given by
 ${v_e} = R\sqrt {\dfrac{8}{3}\pi G\rho } $