Question

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

Answer 1

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`