A particle of mass 10g is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm. Find the work to be done against the gravitational force between them to take the particle far away from the sphere. You may take G = 6.67 x 10⁻¹¹ Nm²kg ⁻²

Given the mass of the sphere M = 100 kg, the mass of the particle m = 10 g or 10⁻² kg, and the radius R = 10 cm or 0.01 m, the initial potential energy (P.E.) of the two bodies is calculated based on their gravitational interaction. When the particle is moved far away from the sphere, the gravitational potential energy of the system becomes zero. The work done in moving the particle from its initial position to an infinite distance is the difference between the final and initial potential energies, resulting in a positive value.

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