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 x 1024 kg) have to be compressed to be a black hole? Option 1) 10-9 m Option 2) 10-6 m Option 3) 10-2 m Option 4) 100 m

For earth to be the black hole, the escape velocity should be at least equal to the speed of light.

$\therefore$ escape velocity = speed of light

$\sqrt{\frac{2GM}{R}}= C$

or $R = \frac{2GM}{C^{2}}$

or $R = \frac{2\times6.67\times10^{11}\times5.98\times10^{24}}{9\times10^{16}}$

$= 8.86\times10^{-3}m$

$R \simeq 10^{-2}m$

Option 1)

10-9 m

This option is incorrect.

Option 2)

10-6 m

This option is incorrect.

Option 3)

10-2 m

This option is correct.

Option 4)

100 m

This option is incorrect.

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