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A cord of length h = 64m is used to conn...

A cord of length h = 64m is used to connect an astronaut (m = 100 kg) to a spaceship (M > > m)which is orbiting near the earth's surface as shown in the figure. Assuming that the spaceship and the astronaut fall on a straight line from the earth's centre, then the tension in the cord is close to [R = 6400 km]

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The tension in the string `T` is given as , `T+F_(gr)=ma_(r )`
`impliesT+(GMm)/((R+l)^(2))=m(R+l)omega^(2)`
`impliesT=m(R+l)omega^(2)-(GMm)/(R^(2))((R )/(R+l))^(2)`
`=m(R+l)(g)/(R )-mg[1+(l)/(R )]^(-2)=(3mgl)/(R )`
`=(3xx100xx10xx64)/(6400xx10^(3))=3xx10^(-2)N`
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