Question 413: Gravitation

Question

A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth (mass = 5.98 $$ 	imes $$ 1024 kg) have to be compressed to be a black hole?

Accepted Answer

From question, Escape velocity
$$ = \sqrt {{{2GM} \over R}}  = c$$ = speed of light
$$ \Rightarrow R = {{2GM} \over {{c^2}}}$$
$$ = {{2 	imes 6.6 	imes {{10}^{ - 11}} 	imes 5.98 	imes {{10}^{24}}} \over {{{\left( {3 	imes {{10}^8}} ight)}^2}}}m$$
= 10
-2
m

Answer

10$$-$$9 m

Answer

10$$-$$6 m

Answer

10$$-$$2 m

Answer

100 m

Gravitation

A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth (mass = 5.98 $ \times $ 1024 kg) have to be compressed to be a black hole?

Choose the correct answer: