Question

In a relation $\sqrt{\frac{2GM}{R}}\ge C$, G stands for universal gravitational constant, M for mass of a very very dense material, R for a small radius and C for velocity of light. Then,

• A. the above relation indicates that orbital velocity is equal to velocity of light.
• B. the above relation indicates something like a black hole.
• C. the above relation indicates that the light is escaping.
• D. the above relation indicates that any object starting from the given mass with speed more than light will return to it.

Answer 1

Answer: (B)

the above relation indicates something like a black hole.

$(\frac{2GM}{R}{)}^{0.5}{V}_e$ is the escape velocity of planet with mass $M$ and radius $R$. If, $V_e$ is greater than speed of light, it means that mass is concentrated in Schwarzschild radius. So, it behaves as the black hole where even light cannot escape its gravitation.