Solve this: 15 A satellite rotating in the same sense as earth in an equatorial orbit has - Physics - Gravitation

Question

Solve this:

15 A satellite rotating in the same sense as earth
in an equatorial orbit has a time period of 6 hours At a certain
instant, it is directly overhead an observer on the equator of
earth It is directly overhead the observer again after a time t The
correct value of t is:

(A) 8 hr (B) 4 8 hr (C) 12 hr (D) 24 hr

Aarushi Mishra · Accepted Answer

It is given that satellite and earth rotates in same senseTsatellite=6 hoursωsatellite=2πTsatellite=2π6rad/hTearth=24 hoursωearth=2πTearth=2π24rad/hAngular velocity of satellite with respect to earth, ωsatellite/earth=ωsatellite-ωearth=2π6-2π24=2π8rad/hLet satellite be overhead again after time t
 When seen from earth the satellite would rotate 2π radians of angle in time t2π8t=2πt=8 hours