25 There is spherical shell of mass M and radius R, the required energy to double its radius is - Physics - Gravitation

Question

25 There is spherical shell of mass M and radius R, the required
energy to double its radius is

Satyendra Singh · Accepted Answer

The gravitational energy or gravitational binding energy of a spherically symmetrical shell is given byEgravitational = 12GM2Rwhere,G = Universal Gravitational constantM = Mass of the shellR = Radius of the shellnow,Initial gravitational energy of the shell = Einitial=  12GM2RFinal gravitational energy when the radius increases to 2R = Efinal = 12GM22R = 14GM2RSince energy finally decreases therefore, the sphere needs to lose = E =  Einitial - EfinalE = 12GM2R - 14GM2RE = 14GM2R
This is the amount of energy needed to be removed from the spherical shell

25.There is spherical shell of mass M and radius R, the required energy to double its radius is