The kinetic energy needed to project a body of mass m from the earth’s surface (radius R) to infinity is

In the given scenario, the initial potential energy of the system is determined by the gravitational interaction between the two masses. When the particle is moved infinitely far away, the potential energy becomes zero. To move the particle from its initial position to infinity, the kinetic energy required is equivalent to the change in potential energy. This kinetic energy can be understood as the work needed to overcome the gravitational attraction between the two bodies. The amount of kinetic energy required is proportional to the gravitational acceleration, the mass of the particle, and the radius of the sphere.

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