Question 7 of 7 Map sapling learning The Schwarzschild radius RBH for an object

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Question 7 of 7 Map sapling learning The Schwarzschild radius RBH for an object of mass M is defined as 2GM where c is the speed of light and G is the universal gravitational constant. RBH gives the radius of the event horizon of a black hole with mass M (in other words, it gives the radius to which some amount of mass M would need to be compressed in order to form a black hole) The mass of the Sun is about 1.99 x100 kg. What would be the radius of a black hole with this mass? Number RBH = The mass of the Earth is about 5.98 x 1024 kg. What would be the radius of a black hole with this mass? Number BH Suppose you want to make a black hole that is roughly the size of an atom (take RsH 1.20 x100 m). What would be the mass M of such a black hole? Number kg Previous Check Answer NextExi Hint

Explanation / Answer

M = 1.99 x 1030 kg

so RBH = 2GM/c2 = 2 (6.67 x 10-11) (1.99 x 1030 ) / (3 x 108)2

RBH = 2949.62 m

for M = 5.98 x 1024 kg

so RBH = 2GM/c2 = 2 (6.67 x 10-11) (5.98 x 1024 ) / (3 x 108)2

RBH = 0.00886 m

for RBH = 1.20 x 10-10 kg

so RBH = 2GM/c2

1.20 x 10-10 = 2 (6.67 x 10-11) M / (3 x 108)2

M = 8.1 x 1016 kg

RBH = 0.00886 m

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