Hydraulic lift, Hollow spherical ball, Objects submerged in water

1. The small piston of a hydraulic lift has a cross-sectional area of 3.00 cm^2 and its large piston has a cross-sectional area of 200 cm^2. What force must be applied to the small piston for the lift to raise a load of 15.0 kN? (In service stations, this force is usually exerted by compressed air.)

2. Small piston of a hydraulic lift (filled with water) has diameter 10 cm.
a) What should be the diameter of the large piston so that the force of 100 N can just balance the male African Elephant (Loxodonta Africana) of mass = 5500 kg at the same level.
b) What additional force needs to be applied to the small piston to lift Elephant to 0.3 m above the previous level?

3. A spherical aluminum ball of mass 1.26 kg contains an empty spherical cavity that is concentric with the ball. The ball just barely floats in water. Calculate (a) the outer radius of the ball and (b) the radius of the cavity.

4. Given are four objects (in attached figure1.jpg) of the same volume. They are all in equilibrium in the tank of water. Rank them according to their masses.

5. Object of mass m and volume V is completely submerged in water by the mass-less, rigid rod attached to the ceiling above open container. What is the tension in the rod when the density of the object is:
a) Half of the water density?
b) Same as the water density?
c) Twice the water density?

6. Mercury is poured into a U-tube (as in attached figure2.jpg). The left arm of the tube has cross-sectional area A1 of 10.0 cm^2, and the right arm has a cross-sectional area A2 of 5.00 cm^2. One hundred grams of water are then poured into the right arm as shown in the figure.
(a) Determine the length of the water column in the right arm of the U-tube.
(b) Given that the density of mercury is 13.6 g/cm^3, what distance h does the mercury rise in the left arm?