Q32 of 38 Page 62

An object of mass m is raised from the surface of the earth to a height equal to the radius of the earth, that is, taken from a distance R to 2R from the centre of the earth. What is the gain in its potential energy?

Given:


Mass of the object = m


Radius of earth = R


Initial height of the object from earth’s centre = R


Final height of the object from earth’s centre = 2R


Let the mass of earth be M. We know that the gravitational potential energy of an object is given by,



Where r is the distance between the object and centre of earth. When the object is at its initial position it is at a distance of R from the centre of the earth. Then its potential energy,



When the object is raised to a height 2R, then the potential energy is given by,



Now the gain in gravitational potential energy is given by




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