Question

Question #1068c

Answer 1

`"Option D"->"~~7.4(km)/s`

Explanation:

Let

• `m->"Mass of satellite"`
• `M->"Mass of Earth"`
• `R->"Radius of Earth" =6400km`
• `h->"Height of the orbit from surface of the Earth" =900km`
• `v->"Orbiting speed of the satellite"`
• `G->"Gravitational constant"`
• `g->"Acceleration due to gravity" =9.8xx10^-3kms^-2`

Now we know

`"Centripetal pull on earth " = "Gravitational force acting between"`

`=>(mv^2)/(R+h)=(GmM)/(R+h)^2`

`=>(cancelmv^2)/cancel(R+h)=(GcancelmM)/(R+h)^cancel2`

`=>v^2=(GM)/(R+h))`

`=>v^2=(gR^2)/(R+h)......(1)` `" "[ Since " " GM=gR^2]`

Now inserting the values in equation (1) we get

`=>v^2=(9.8xx10^-3(6400)^2)/(6400+900)`

`=>v=sqrt((9.8xx10^-3(6400)^2)/(6400+900))~~7.4(km)/s`