1 Black Hole (10 points) The Schwarzchild radius R characterizes a black hole. L
ID: 1791138 • Letter: 1
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1 Black Hole (10 points) The Schwarzchild radius R characterizes a black hole. Light within distance R of the black hole's center cannot escape its gravitational pull. The Schwarzchild radius R depends on the mass M of the black hole, the speed of light e, and Newton's gravitational constant G. (The values of G and e are on the formula sheet.) Based on dimensional analysis, which of the following expressions could be the Schwarzchild radius? A, R = Me B. R2 - GM D. R-GMe E. None of the above can be correct Briefly justify your response. 2 Quarter Mile (10 points) Starting from rest, a Tela Roadster can (omplete a quarter mile race (402 ) in 13.4 e. (a) What is the average speed of the car over the quarter mile? (b) Assuming the car accelerates at a constant rate, what is its acceleration? 06 3 Newton (10 points) (a) A spaceship with a mass of 20,000 kg is travelling in a straight line at a constant speed of 300 m/s in deep space, far from any planets or stars. Its rocket engines must be firing. True or FalseExplanation / Answer
Dimensional formula of radius is M0L1T0
Dimensional formula of Mass is M1L0T0
Dimensional formula of speed is M0L1T-1
Dimensional formula of gravitational constant is M-1L3T-2
Let expression of R be MxcyGz
Equating the dimesions of R to dimensions of it's expression we get
0 = x-z
1=y+3z
0=-y -2z
Solving these euations we get,
x = 1, y = -2 z=1
so R = GM/c2
option C is correct.
2) Average speed = distance /time = 402/13.4 = 30 m/s
At cosntant acceleration,
s = ut + 1/2 (at2)
initial speed, u is zero
402 = a *13.42 /2
a 4.5 m/sec2
3) As space ship is not near any planets or stars, there is no force acting on it. With no external force and moving with constant velcocity, roccket engines are not firing.
Statement is false
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