You are exploring a small moon of a distant planet. Measurements indicate that this moon is a sphere of uniform density rho = 5000 kg/m3. You dig a very deep hole into the moon that reaches within r0 = 1000 m of the center of the moon. With your spacesuit, you have a mass of m = 85 kg. Find the force of gravity on you when you stand at the bottom of the hole.

Which is an example of gaining a static charge by conduction? a) rubbing a balloon against your hair. b) shuffling your shoes across a carpet. c) bringing a charged rod near an electroscope. d) touching your car on a cold day and getting a shock.

Which law represents the thermodynamic statement of the conservation of energy of a system? a. the fourth law b. the first law c. the second law d. the third law

Suppose water is leaking from a tank through a circular hole of area ah at its bottom. when water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to cah 2gh , where c (0 < c < 1) is an empirical constant. a tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom. (assume the removed apex of the cone is of negligible height and volume.) (a) suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. the differential equation governing the height h in feet of water leaking from a tank after t seconds is dh dt = − 5 6h3/2 . if the height of the water is initially 8 feet, how long will it take the tank to empty? (round your answer to two decimal places.)