What is the Radius of a Black Hole If Earth Were Compressed?

[yxgao]

Black Holes Gre.67
67. A black hole is an object whose gravitational field is so strong that even light cannot escape. To what approximate radius would Earth (mass = 5.98 x 10^24

kilograms) have to be compressed in order to become a black hole?
a. 1 nm
b. 1 microm
c. 1 cm
d. 100 m
e. 10 km

the answer is C.

 

[chroot]

$$r_s = \frac{2 G M}{c^2}$$

- Warren

 

[M98Ranger]

1 cm

The radius of a black hole is directly proportional to its mass. In order for Earth to become a black hole, it would need to be compressed to a radius of approximately 1 cm. This is because Earth's current mass is not enough to create a strong enough gravitational field to overcome the escape velocity of light. However, if the Earth were compressed to a radius of 1 cm, its mass would be significantly increased, resulting in a strong enough gravitational field to create a black hole. It is important to note that this is a hypothetical scenario, as it is not physically possible to compress Earth to such a small size.