Black holes are objects whose gravitational field is so strong that not even lig

Question

Black holes are objects whose gravitational field is so strong that not even light can escape. One way of thinking about this is to consider a spherical object whose density is so large that the escape speed at its surface is greater than the speed of light, c. If a star's radius is smaller than a value called the Schwarzschild radius Rs, then the star will be a black hole, that is, light originating from its surface cannot escape. (a) For a nonrotating black hole, the Schwarzschild radius depends only upon the mass of the black hole. Show that it is related to that mass M by Rs (2GM)/c2. (Do this on paper. Your instructor may ask you to turn in this work.) (b) Calculate the value of the Schwarzschild radius for a black hole whose mass is ten solar masses. km

Explanation / Answer

for any object to esacape from the gravitational influence of Planet ro any other big mass

its KE must be grater than its potential energy.

suppose R is the radius of the planet

PE of the object on its surface = GMm/R

If u is its initial velocity KE = mu2/2

>= GMm/R

u >= (2GM/R)1/2

if c < (2GM/R)1/2  , then even light or any objects moving at the speed of light cannot escape the planet with mass M and radius R

hence Rs = 2GM/c2? , Schwarzchild radius.

M = 10 *2.0e+30 kg ( 10 solar masses)

Rs? = 2*6.67e-11*2.0e+31 / 9.0e+16

   = 2.96e+4 m = 29.6 km

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