Question

If very the escape velocity from the surface of the earth then the escape velocity from the center of the earth

Answer 1

Answer:

To calculate gravitational potential at the center of earth, take a spherical shell element at radius r. 

dV=−rGM34πR34πr2dr=−R33GMrdr

Integrating this, we get V=−23RGM 

The potential at the surface of earth is −RGM

Since escape velocity is proportional to the square root of potential energy and hence square root of gravitational potential, escape velocity at centre of earth will be 23ve