A particle of mass 50g is kept on the surface of uniform sphere of mass 120kg and radius 50cm.Find the work to be done against the gravitational force between them to take the particle far away from the sphere.An artificial satellite is moving in a circular orbit around earth with a speed equal to half the magnitude of escape velocity from earth .1. Determine the hieght of the satellite above the earth's surface2.If the satellite is topped suddenly in its orbit and allowed to fall freely towards the earth, find the speed with which it hits the surface of the earth.
Here,
Mass of sphere, M = 120 kg
Radius of the sphere, r = 50 cm = 0.5 m
Mass of particle, m = 50 g = 0.05 kg
Now,
Potential energy of the particle at the surface of the sphere, P1 = -GMm/r
Potential energy of the particle at infinity, P2 = -GMm/infinity = 0
Work done = change in potential energy = P2 – P1 = GMm/r
= (6.67 × 10-11)(120)(0.05)/0.5
= 8.004 × 10-10 J