Question

Given a homogenous sphere with density rho. For the case where the radius R of the sphere is exactly 2GM/c² (meaning when the sphere is a black hole), express R in terms of rho. For a rho given in units of 1gcm^-1, determine R in light seconds.

Answer 1

As Volume of sphere is:

If density is rho

Mass of sphere is:

NOw, as we need

Put value of mass in this equation:

hence, denisty is given as:

NOw we can express R in terms of rho as:

Now, speed of light is 'c'

time taken to cover distance R with speed c is:

T = R/c

hence, we can write distance R as time seconds as:

Which is as required.