(a) Show that a black hole attracts an object of mass m with a force of mc?2?R?S/(2?r?2), where ?r is the distance between the object and the center of the black hole. (b) Calculate the magnitude of the gravitational force exerted by a black hole of Schwarzschild radius 14.0 mm on a 5.00-kg mass 3000 km from it. (c) What is the mass of this black hole?

Solution Step 1 A)In this problem we should calculate the mass of the object m with a force of mc2RS/2r2 To find value of M blackhole 2 R s 2GM /c bh 2 = M bh = c R s2G c2Rs 2 2 G( 2G/R2)m = mc R /2s 2 2 2 2 mc R /2Rs= mc R /2r s