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Gravitation question

2014 · Q148
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Gravitation question

2014 · Q148

NEETPhysicsGravitationMCQ+4 / −1
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× 1024 kg) have to be compressed to be a black hole?
  1. A
    10−-−9 m
  2. B
    10−-−6 m
  3. C
    10−-−2 m
  4. D
    100 m
View written solutionFree

Correct answer: C

From question, Escape velocity

=2GMR=c = \sqrt {{{2GM} \over R}} = c=R2GM​​=c = speed of light

⇒R=2GMc2 \Rightarrow R = {{2GM} \over {{c^2}}}⇒R=c22GM​

=2×6.6×10−11×5.98×1024(3×108)2m = {{2 \times 6.6 \times {{10}^{ - 11}} \times 5.98 \times {{10}^{24}}} \over {{{\left( {3 \times {{10}^8}} \right)}^2}}}m=(3×108)22×6.6×10−11×5.98×1024​m

= 10-2 m

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