My Notes Ask Your Teacher holes are objects whose gravitational field is so stro

Question

My Notes Ask Your Teacher holes are objects whose gravitational field is so strong that not even I light can escape. One way of thinking about this is to consider a spherical object whose at its surface is greater than the speed of light, c. If a star's radius is smaller than a value called the Schwarzschild radlus R, then the star will be a bilsck hole, that is, light originating from its density is so large that the escape surface cannot escape (a) For a nonrotating black hole, the Schwarzschild radius depends only upon the nstructor may ask you to turn in this work) mass of the bleck hole. Shothtr tothat mass M by R caomye (Do this on paper, Yyour (b) Calcuate the value of the Schwaraschid radius for a black hole whose mass is ten soler masses km

Explanation / Answer

Solution:

a) From the conservation of energy , 1/2 mv^2 = G M m/R

=> R = 2 GM / v^2

For a black hole , whose velocity is >=c, Rs= 2 GM /c2 .

b) If M = 10 Msun = 10 * (2e30) kg = 2 e31 kg

Schwarzchild radius = Rs = 2(6.67x10-11) (2 x1031) /(3x108)2 .

= 29.6 km

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