Calculate the average density of the Earth

[LokeshCBSE]

1. Calculate the average density of the Earth.
2. Derive how does the value of gravitational force F between two objects change when
   • distance between them is reduced to half and
   • mass of an object is increased four times.

[LokeshCBSE]

1. Suppose, the radius of Earth is R, then its volume will be
   
2. • Let gravitational force be F when the distance between them is R,
     …(1)
     Now, when the distance reduces to half,
     …(2)
     On dividing Eq. (1) by Eq. (2), we get
     
   • When the mass becomes 4 times,