First slide

Gravitaional potential energy

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 x 10²⁴ kg) have to be compressed to be a black hole

Moderate

A

10^-9 m
B

10^-6 m
C

10^-2 m
D

100 m

Solution

Escape velocity $v = \sqrt{\frac{2 GM}{R}} = c =$ speed of light
$\Rightarrow R = \frac{2 GM}{c^{2}} = \frac{2 \times 6 .6 \times 10^{- 11} \times 5 .98 \times 10^{24}}{{(3 \times 10^{8})}^{2}} m$
= 10^-2 m

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