Assertion (A): The kinetic energy needed to project a body of mass m from the Earth's surface to infinity is (1/2)mgR, where R is Earth's radius. Reason (R): The maximum gravitational potential energy of the body is zero at infinity. Choose the correct answer.
Options

Question

Assertion (A): The kinetic energy needed to project a body of mass m from the Earth's surface to infinity is (1/2)mgR, where R is Earth's radius. Reason (R): The maximum gravitational potential energy of the body is zero at infinity. Choose the correct answer.

Options

G1 Physics · Accepted Answer

Taking gravitational potential energy to be zero at infinity: At Earth's surface, U = -GMm/R. For minimum escape, final speed at infinity is zero, so total final energy is zero. Therefore the required initial kinetic energy is K = GMm/R. Since g = GM/R², we have GMm/R = mgR. Thus the required kinetic energy is mgR, not (1/2)mgR. Assertion A is false. At infinity, gravitational potential energy approaches zero, so Reason R is true. Correct option: B.