Exercise 12.2
A cube 6.0
on each side is made of a metal alloy. After you drill a cylindrical hole 3.0
in diameter all the
way through and perpendicular to one face, you find that the cube weighs 6.70
.
Part A
What is the density of this metal?
Express your answer with the appropriate units.
Correct
Part B
What did the cube weigh before you drilled the hole in it?
Express your answer with the appropriate units.

Part A
A oneinch depth of sand is poured onto the cap on each arm. After the caps have moved (if necessary) to
reestablish equilibrium, is the right cap higher, lower,
or the same height as the left cap?
Hint 1.
Pressure at the surface
The pressure at the base of each arm depends on the pressure at the surface of each arm, not the
weight at the surface of each arm.
Hint 2.
Evaluate the weight of the sand
Compare the weight of the sand on the two caps. Which of the following is true?
Hint 3.
Evaluate the pressure applied by the sand
Now compare the pressure exerted by the sand on the two caps. Which of the following is true?

Correct
Although one inch of sand on the right cap is much heavier than one inch of sand on the left cap, the
pressures exerted by the sand are the same on both caps. Since the pressures exerted by the sand are
equal, the pressures at the base of each arm due to the water must be equal. This requires equal heights
of water in the two arms.