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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

User ZuTa
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Answer:B

Step-by-step 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


(GMM_x)/(r_x^2)=(GMM_y)/(r_y^2)

cancel out the common terms we get


(M_x)/(r_x^2)=(M_y)/(r_y^2)


(M_x)/(M_y)=((r_x)/(r_y))^2


(M_x)/(M_y)=((140)/(581))^2


(M_x)/(M_y)=0.05806\approx 0.0581

User Ali Malek
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