The kinetic energy needed to project a body of mass m from the earth's surface to infinity is :

Explanation

This is the following solution: The correct option is mgR: The kinetic energy needed to project a body of mass m from the Earth's surface to infinity is equal to the initial potential energy of the body, which is mgR.When an object is on the surface of the Earth, it has gravitational potential energy due to its position relative to the Earth's center. The gravitational potential energy is given by the equation PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height or distance from the reference point. In this case, the reference point is taken to be at infinity.At the Earth's surface, the height or distance from the reference point (infinity) is R, which is the radius of the Earth. Therefore, the initial potential energy of the body is given by PE = mgh = mgR.As the body is projected from the Earth's surface to infinity, the potential energy is converted into kinetic energy. At infinity, the gravitational potential energy becomes zero, and the entire energy of the body is in the form of kinetic energy.