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Llana [10]
3 years ago
5

An astronaut is in equilibrium when he is positioned 140 km from the center of asteroid C and 581 km from the center of asteroid

Y, along the straight line joining the centers of the asteroids. What is the ratio of the masses X/Y of the asteroids?A. 17.2B. 0.0581C. 0.241D. 4.15
Physics
1 answer:
serg [7]3 years ago
8 0

Answer:B

Explanation:

Given

Distance of astronaut From asteroid x is r_x=140 km

Distance of astronaut From asteroid Y is r_y=581 km

Suppose M,M_x,M_y be the masses of Astronaut , asteroid X and Y

If the astronaut is in equilibrium then net gravitational force on it is zero

F_x=F_y

\frac{GMM_x}{r_x^2}=\frac{GMM_y}{r_y^2}

cancel out the common terms we get

\frac{M_x}{r_x^2}=\frac{M_y}{r_y^2}

\frac{M_x}{M_y}=(\frac{r_x}{r_y})^2

\frac{M_x}{M_y}=(\frac{140}{581})^2

\frac{M_x}{M_y}=0.05806\approx 0.0581

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