What would happen if the sun suddenly became a black hole without changing its mass?
1 answer:
Answer:
It would shrink to a radius of 2.95 km
Explanation:
In order to be a black hole, the Sun must shrink so that its radius becomes equal to its Schwarzschild radius:
where
G is the gravitational constant
is the mass of the Sun
c is the speed of light
Substituting into the equation, we find
So, the Sun should shrink to a radius of 2.95 km.
You might be interested in
Answer:
Explanation:
Given that
I= ∫r²dm
We need to integrate over the volume of the disc, which is not smart enough, so we brake the disc into rings and integrate from the center r=0 to r=R, as shown in attachment
Since we know the moment of inertial of a ring to be
I=mr²
We cannot integrate the r² with respect to m, so we are going to write dm as a function of r
dm
So we assume that
The ratio of the area of the rings to the whole disc is equal to ratio of their masses.
dm/M=2πrdr/πR²
Therefore,
dm=2rM/R² dr
So we are going to replace dm in the integral
I= ∫r²dm
I= ∫r²(2rM/R²) dr. From 0 to R
Where 2, M and R are constant,
I= 2M/R² ∫r³dr. From r=0 to r=R
I= 2M/R² (r⁴/4) From r=0 to r=R
I=2M/R² (R⁴/4 - 0)
I=2M/R² × R⁴/4
I=MR²/2.
This is the moment of inertial of the disc and it doesn't depend on the thickness of the disc.
