Question 397: 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 $ 10
24
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 10 24 kg) have to be compressed to be a black hole?

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