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Gravitation — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysicsGravitation2 Marks
Question
A black hole is a body from whose surface nothing may ever escape. What is the condition for a uniform spherical mass M to be a black hole? What should be the radius of such a black hole if its mass is the same as that of the Earth?
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Answer

For a body to be a black hole, the escape velocity should be such that even light cannot escape. The limiting case for escape velocity is,
$\sqrt{\frac{2\text{GM}}{\text{R}}}\leq\text{c}(\text{speed of light})$
For our earth, M = Me = 6 × 1024kg,
$\text{R}=\frac{2\text{GM}}{\text{c}^2}=9\times10^{-2}\text{m or }9\text{cm}$

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