A particle of mass 10 g 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 takr G = 6.67 x 10⁻¹¹ Nm² kg⁻²

To calculate the work required to move a particle away from a sphere, we consider the gravitational potential energy between the two. The particle has a mass of 10 g (0.01 kg), and the sphere has a mass of 100 kg with a radius of 10 cm (0.1 m). The work done is equivalent to the energy needed to overcome the gravitational attraction and take the particle far away, where gravitational potential energy becomes zero.

Gravitational potential energy is determined by the masses involved, the gravitational constant G = 6.67 x 10⁻¹¹ Nm² kg⁻², and the distance between the centers of mass. At the sphere’s surface, this distance is equal to the sphere’s radius (0.1 m).

Substituting the given values into the formula for gravitational potential energy, the calculation shows that the work required to take the particle far away is 6.67 x 10⁻¹⁰ J. This value represents the energy needed to overcome the gravitational pull between the sphere and the particle.

Hence, the work to be done is 6.67 x 10⁻¹⁰ J, reflecting the small but measurable gravitational interaction between the particle and the sphere due to their masses and proximity.