If the satellite is stopped suddenly in its orbit and is allowed to fall freely into the earth's surface with what speed it hits the surface of earth?

Options

A. `7.92 km//s`
B. `11.2" km s"^(-1)`
C. `8.92" km s"^(-1)`
D. `5.6" km s"^(-1)`

Answer

A

Explanation

Here total energy at height h = Total energy at surface
`0-(GMm)/(R+h)=(1)/(2)mv^(2)-(GMm)/(R )`
`(1)/(2)mv^(2)=(GMm)/(R )-(GMm)/(R+R)=(GMm)/(2R)`
`v=sqrt((GM)/(R ))=sqrt(gR)=sqrt(9.8xx6400xx10^(3))`
`x=7.92 kms^(-1)`.
Correct choice is (a).