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>> $A black hole is an object whose gravitat$

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 $(m a s s = 5.98 \times 1 0^{24} k g)$ have to be compressed to be a black hole?

A

$1 0^{- 9}$ m

B

$1 0^{- 6}$ m

C

$1 0^{- 2}$ m

D

$100 m$

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Updated on : 2022-09-05

Solution

Verified by Toppr

Correct option is C)

For earth to be black hole the escape velocity should be at least equal to speed of light.
$∴$ escape velocity $=$ speed of light
$\frac{2 G M}{R} = C$

$R = \frac{2 G M}{C ^{2}}$

$R = \frac{2 \times 6 . 6 7 \times 1 0 ^{- 11} \times 5 . 9 8 \times 1 0 ^{24}}{9 \times 1 0 ^{16}} = 8.86 \times 10^{- 3} m = 10^{- 2} m$

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