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13 Dec 2019

Show that a black hole attracts an object ofmass m with aforce of

mc2Rs/(2r2)
where r is the distance between the objectand the centerof the black hole.

(b) Calculate the magnitude of the gravitational force exerted byablack hole of Schwarzschild radius 13.86 mm on a 5.10-kg mass 4978km from it.

(c) What is the mass of this black hole?

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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

Black holes are objects whose gravitational field is so strong thatnot even light can escape. One way of thinking about this is toconsider a spherical object whose density is so large that theescape speed at its surface is greater than the speed of light, c.If a star's radius is smaller than a value called the Schwarzschildradius Rs, then the star will be a black hole, that is, lightoriginating from its surface cannot escape.
(a) For a nonrotating black hole, the Schwarzschild radius dependsonly upon the mass of the black hole. Show that it is related tothat mass M by Rs = (2GM)/c2.
(b) Calculate the value of the Schwarzschild radius for a blackhole whose mass is ten solar masses.
-----(ANSWER in km)

P.S. The problem gives the hint "Use conservation of energy, and anescape speed equal to the speed of light to derive the expressionfor the Schwarzchild radius of a non-rotating black hole."

Thank you so much for any help!

<p>The radius (Rh) and mass (Mh) of a black hole are relatedby Rh = 2GMh/c squared, where (c) is the speed of light. Assumethat the gravitational acceleration (ag) of an object at a distance(ro)= 1.001(Rh) from the center of a black hole is given by (ag) =G M / r squared (it is, for large black holes).</p>
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<p>B. &#160;If an astronaut with a height of 1.73 m is atrowith her feet toward this black hole, what is the difference ingravitational acceleration between her head and her feet?</p>

A spacecraft in the shape of a long cylinder has a length of 100 m, and its mass with occupants is 1 000 kg. It has strayed too dose to a black hole having a mass 100 times that of the Sun (Fig. P13.7). The nose of the spacecraft points toward the black hole and the distance between the nose and the center of the black hole is 10.0 km. (a) Determine the total force on the spacecraft. (b) What is the difference in the gravitational fields acting on the occupants in the nose of the ship and on those in the rear of the ship, farthest from the black hole? (This difference in accelerations grows rapidly as the ship approaches the black hole. It puts the body of the ship under extreme tension and eventually tears it apart.) 

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