Question

What is Schwarzschild radius?
 $
  \left( {\text{A}} \right)\dfrac{{GM}}{{{V^2}}} \\
  \left( {\text{B}} \right)\dfrac{{GM}}{{2{V^2}}} \\
  \left( {\text{C}} \right)\dfrac{{2GM}}{{{c^2}}} \\
  \left( {\text{D}} \right)\dfrac{{GM}}{{2{c^2}}} \\
  $

Answer 1

Hint : There is no specific solution or derivation required to solve this kind of questions. You can directly write down the value of Schwarzschild radius and mention all the parameters used in the equation and their meanings. You can also mention where Schwarzschild radius is used in different scientific experiments.

Complete Step By Step Answer:
Karl Schwarzschild had found an exact solution to Einstein's field equation for the gravitational field outside a non-rotating spherically symmetric body with mass M.
The Schwarzschild solution describes the space time under the influence of a massive, spherically symmetric, non-rotating object.
The radius of the spherical body where the escape velocity was equal to the speed of light was called Schwarzschild radius.
The Schwarzschild radius is given by
 $ {r_s} = \dfrac{{2GM}}{{{c^2}}} $
where G = Gravitational constant,
M = Mass of the object,
c = Speed of light.
Hence the answer to our question is option (B) $ {r_s} = \dfrac{{2GM}}{{{c^2}}} $ .

Note :
Schwarzschild radius is also referred to as gravitational radius. Schwarzschild radius is diversely used by scientists for various inventions. It is used to approximate the Gravitational time dilation near a large, slowly rotating, nearly spherical body such as earth or sun. Also to find Newtonian gravitational fields near large, slowly rotating, nearly spherical bodies and much more.