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.
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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