Question

Given a homogenous sphere with density rho. For the case where
the radius R of the sphere is exactly 2GM/c^{2} (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.

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