A black hole is an object whose gravitational field is so strong … - Vidyadip

MCQ

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?

A
$10^{-9} \,\,m$
B
$10^{-6}\,\,m$
✓
$10^{-2} \,\,m$
D
$100 \,\,m$

✓

Answer

Correct option: C.

$10^{-2} \,\,m$

c
Light cannot escape from a black hole,

${v_{esc}} = c$

$\sqrt {\frac{{2GM}}{R}} = c\,\,\,\,\,or\,\,\,\,\,\,\,R = \frac{{2GM}}{{{c^2}}}$

$R = \frac{{2 \times 6.67 \times {{10}^{ - 11}}N{m^2}k{g^{ - 2}} \times 5.98 \times {{10}^{24}}kg}}{{{{\left( {3 \times {{10}^8}\,m\,{s^{ - 1}}} \right)}^2}}}$

$ = 8.86 \times {10^{ - 3}}m \approx {10^{ - 2}}\,m$

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