A cord of length 4 m is used to connect a 100 kg astronaut to spaceship whose mass is much larger than that of the astronaut. Estimat the value of the tension in the cord. Assume that the spaceship is orbiting near earth surface. A ssume that the spaceship and th eastronaut fall on a straight line from the earth centre. The radius of the earth is 6400 km.

Answer

`T=3xx10^(-2)N`

Explanation

Cemtripetal force for orbiting of sface ship is provided by gravitational force.
`(GM M_(e ))/(R^(2))=Mromega^(2) rArr omega = sqrt((GM_(e ))/(R^(3)))` …(i)
For orbitting of astronaut
`F_(g)+T=m(R+L)omega^(2) rArr (GM_(e )m)/((R+L)^(2))+T=m(R+L)((GM_(e ))/(R^(3)))`
`T=m(R+L)(GM_(e ))/(R^(3))-(GM_(e )m)/((R+L)^(2))`
`T = m(R+L)(gR^(2))/(R^(3))-(mgR^(2))/((R+L)^(2)) rArr T = mg+(mgL)/(R )-mg+(2mgL)/(R )`
`T = (3mgL)/(R )rArr T = (3xx100xx10xx64)/(64xx10^(5))rArr T=3xx10^(-2)N`