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7.Gravitation
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If $M$ is mass of a planet and $R$ is its radius then in order to become black hole [ $c$ is speed of light]
A
$\sqrt{\frac{G M}{R}} \leq c$
B
$\sqrt{\frac{G M}{2 R}} \geq c$
C
$\sqrt{\frac{2 G M}{R}} \geq c$
D
$\sqrt{\frac{2 G M}{R}} \leq c$
Solution
(c)
A planet can become a black hole if its mass and radius are such that it has an immense force of gravity on its surface. The force of attractum has to be so large that even light cannot escape from its surface.
Speed of light $=c$
$v_\theta=\sqrt{\frac{2 G M}{R}}$
If $v_e \geq c$
$\Rightarrow$ Even light can't escape from the surface of such planet making it appear black.
Standard 11
Physics
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