The critical speed of a satellite orbiting very close to the surface of the earth is `[g=10 m//s^(2)` and `R=6.4xx10^(-6)m]`

Options

A. `8xx10^(3)m//s`
B. `4xx10^(3)m//s`
C. `16xx10^(4)m//s`
D. `2xx10^(4)m//s`

Answer

A

Explanation

For a satellite orbiting very close to the surface of the earth, the critical speed,
`v_(e )=sqrt((GM)/(R ))` but `GM = gR^(2)`
`therefore v_(C )=sqrt((gR^(2))/(R ))=sqrt(gR)=sqrt(10xx6.4xx10^(6))`
`therefore v_(C )=sqrt(64xx10^(6))=8xx10^(3)m//s`