Question #1068c

1 Answer
Jun 5, 2016

Answer:

#"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#