Question

What will be the corresponding expression for the energy needed to completely disassemble the planet earth against the gravitational pull among its constituent particles? [Assume the earth to be sphere of uniform mass density. Calculate this energy, given the product of the mass and the radius of the earth to be $2.5 \times 10^{31} kg m$.]

Answer 1

Answer:

Explanation: Let us suppose that earth is made of a infinite numbe of very thin concetric spherical shells. it can be completely disassemble by removing these shells one by one.

The study of earth when only a sphere of radius x is left and find the energy required  to remove  a shell  of thickness dx

Now potential of this sphere x is u= Gm/x

Now work done  to remove a shell of thickness dx would be equal  to the change in potential energy = Gm dm /x

where dm = mass of shell = 4 πx²dxp

dw =( 4/3x³p) (4π x²dxp;)/x

16 /3 Gn²p²x⁴dx...

On substituting the given vaue is 3/5 Gm²/r = 3/5 g MR

= 1.5 ×10³²