A geo-stationary satellite is orbiting the earth at a height at a above the surface of the earth, R being the radius of the earth. The time period of another satellite at a height of 2.5R from the surface of earth is

The time period of a satellite orbiting at a distance r from the centre of the earth is given byT2=4π2r3GM2For two satellites at distances r1 and r2, we haveT1T2=r1r23/2or T2=T1r2/r13/2For geostationary satellite,T1 =1day =24hoursand r1=6R+R=7RFor other satellite r2=2⋅5R+R=3⋅5R∴ T2=24×(3⋅5R/7R)3/2=24×(1/2)3/2                                              =62 hours