An 80-kg hiker climbs to the top of a tall hill and builds up 470,000 J of gravitational potential energy. How high did the hike
2 answers:
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A.
The orbital speed of the clumps of matter around the black hole is equal to the ratio between the circumference of the orbit and the period of revolution:
where we have:
is the orbital speed
r is the orbital radius
is the orbital period
Solving for r, we find the distance of the clumps of matter from the centre of the black hole:
B.
The gravitational force between the black hole and the clumps of matter provides the centripetal force that keeps the matter in circular motion:
where
m is the mass of the clumps of matter
G is the gravitational constant
M is the mass of the black hole
Solving the formula for M, we find the mass of the black hole:
and considering the value of the solar mass
the mass of the black hole as a multiple of our sun's mass is
C.
The radius of the event horizon is equal to the Schwarzschild radius of the black hole, which is given by
where M is the mass of the black hole and c is the speed of light.
Substituting numbers into the formula, we find
Answer:
1917723.40119 m/s
Explanation:
m = Mass of deuteron =
k = Boltzmann constant =
T = Temperature =
RMS velocity is given by
The RMS velocity of the deutrons is 1917723.40119 m/s