Schwarzschild radius (sometimes referred to as the gravitational radius) is the

Question

Schwarzschild radius (sometimes referred to as the gravitational radius) is the distance from the center of an object such that, if all the mass of the object were compressed within a sphere of such radius, the escape speed from the surface would equal the speed of light. It, thus, defines a spherical boundary called the event horizon, commonly associated with black holes, beyond which the events cannot affect an outside observer. Theoretically, any amount of matter will become a black hole if compressed into a space that fits within its corresponding Schwarzschild radius. Using equation for the escape velocity vecae Schwarzschild radius: raboxald From this expression you can see that the Schwarzschild radius depends only on the object's mass. 2GM 8 and setting it equal to the speed of light vescapec3x 10s m/s, we can find the 2GM Estimate the Schwarzschild radius for a mini-black hole formed when a super-advanced civilization decides to punish you (unfairly) by squeezing you until you became so small that you disappear inside your own event horizon. Assume your mass to be 70 kilograms (i.e. you weigh about 150 Ibs) meters (use scientific notation and round the coefficient to two decimals). How does this compare with the radius of a proton which is about 8.8 x 10-16 m? Type "true" or "false" next to each statement below. my Schwarzschild radius is a lot bigger than a proton my Schwarzschild radius is somewhat bigger than a proton my Schwarzschild radius is about the same size as a proton my Schwarzschild radius is a somewhat smaller than a proton my Schwarzschild radius is a lot smaller than a proton

Explanation / Answer

Schwarzschild radius of person weight 70 kg can be find out by using

rschwarzschild   = (2 G M ) / c2  

here G = Universal Gravity Constant = 6.754 x 10-11 m3kg1s2

M = Mass of the person = 70 kg

c = Speed of the light = 3 x 108 m/s

On substituting all values we get

rschwarzschild   = [(2) (6.754 x 10-11 m3kg1s2 )( 70 kg)] / [(3 x 108 m/s)2 ]

rschwarzschild = 105.062 x 10-27 m

rschwarzschild = 1.05 x 10-25 m

The above value is a lot smaller than the radius of the proton which is about to 8.8 x 10-16 m

my Schwarzschild radius is a lot bigger than proton : false

my Schwarzschild radius is somewhat bigger than proton :  false

my Schwarzschild radius is about the same size as a proton :  false

my Schwarzschild radius is somewhat smaller than proton :  false

my Schwarzschild radius is a lot smaller than proton : true .

  

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