If a wristwatch is placed on ground (or rather ice) face up at south pole?

Question

how many revolutions will hour hand make with respect to stars in one day?

Lets ignore small difference between siderial day and solar day.

Answer 1

The hour hand turns 'clockwise' at 2 turns per day. That is a rate of 30 degrees per hour (360 in 12 hours)

The stars (seen from the South pole) appear to turn counterclockwise, one turn per day. That is a rate of 15 degrees per hour, the other way.

If we start the chronometer just as the hour hand points to a star, one hour later the angle will be 45 degrees. Twenty four hours later, the total angle will be 24 times 45 = 1080 degrees (3 whole turns)

Answer 2

Raymond is right. If the watch were face-up on the NORTH pole, its hour hand would rotate in the same direction as the apparent motion of the stars. However, at the SOUTH pole, the watch is facing in the opposite direction and its hands would rotate counter to the direction of the stars. A 12-hour watch with hands would therefore rotate (about) three times in a day with respect to the stars.

Answer 3

IT REVOLVE'S COMPLETLY 1440 EVERY 24 HOUR'S...