NEET Physics Question - Gravitation - Gravitational Potential Energy

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 $= 5.98 \times 10^{24}\text{ kg}$) have to be compressed to be a black hole?

(2014)

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

$10^{-6}\text{ m}$

$10\text{ m}$

$100\text{ m}$

Solution:

For a black hole, the escape velocity equals the speed of light $c$, leading to the radius formula $R = \frac{2GM}{c^2}$. Substituting the gravitational constant, mass of earth, and speed of light gives $R \approx 10^{-2}\text{ m}$. Thus, option A is correct.

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