A Black hole is a body from whose surface nothing may evan escape. What is the condition for an uniform spherical body of amss M to be a black hole? What should be the radius of such a black hole if its mass is nine times the mass of the earth?

A black hole is a collapsed massive body under its own gravity to a point where its escape velocity exceeds the speed of light. For an object to be a black hole, it must satisfy the condition known as the Schwarzschild radius, which defines the size of the event horizon-the boundary beyond which nothing can escape.

The condition for a uniform spherical body of mass M to be a black hole is that the radius must be less than or equal to the Schwarzschild radius. Now, the Schwarzschild radius, or rₛ, is directly proportional to the mass of the body and can be easily expressed in terms of its mass. A body, when its radius is equal to its Schwarzschild radius, is a black hole.

If we take a black hole of mass nine times the Earth’s mass, we can calculate its Schwarzschild radius. Earth’s mass is about 5.97 x 10²⁴ kilograms. Therefore, the mass of the black hole would be 9 x 5.97 x 10²⁴ kg. Using the formula for the Schwarzschild radius, we can calculate the particular radius for this black hole. This radius will set the point at which the speed of escape equals the speed of light and thus form a black hole.