The fact that the two objects are balanced in Question #2 tells you that they both have the same weight.  In order to have the same weights they must have the same mass.

The wood is floating.  It must have a density less than water.  Density is mass/volume.  You can compute the density of the wood by dividing its mass, 27 g, by its volume, 30 cm³.  The density is 0.9 g/cm3.  The density of the rock is greater than water.  The density of the rock is 12 g/ 9 cm³ or 1.67 g/cm³.

Typical sea level pressure is 14.7 pounds per square inch which is about 1000 mb, 30 inches of mercury, or 1 bar.  1 bar is therefore about 15 psi.


Pressure at any level in the atmosphere is determined by the weight of the air overhead.  As you move upward in the atmosphere there is less and less air above, less and less weight, pressure decreases with increasing altitude.  Pressure decreases most rapidly with increasing altitude in dense air.  The densest air in the atmosphere is found at ground level.


The red shaded portion in the barometer (between A and C) acts like a balance.  The pressure produced by the weight of a column of air above and pushing down on Point C is balanced by the weight and pressure of the mercury column extending from C to D (shaded orange).  The pressures at Points A anc C are equal.  We assume there is no pressure pushing down on the top of the mercury column at Point D.

Pressure decreases with increasing altitude.  The pressure at Point A will be a little higher than the pressures at the middle and top of the balloon.  The numbers (15, 14.5, and 14) were added to illustrate the decrease of pressure with increasing altitude.


A balloon will expand or shrink in order to keep the pressure of the air inside the balloon equal to the pressure of the air outside the balloon.  Heating the air in a balloon would momentarily increase the pressure of the air in the balloon and the balloon would expand (we will assume that this happens so quickly that pressure essentially remains constant).  Air hasn't been added to or removed from the balloon.  As the balloon expands and its volume increases, the density will decrease.  Air pressure remains constant.


Ordinarily adding air to a balloon would momentarily increase the pressure.  But we cool the air at the same time.  Cooling the air would momentarily decrease the pressure.  So it would be possible to add air and cool the air at the same time and keep the pressure constant.  If the pressure remains constant there is no reason for the balloon to expand or shrink, thus the volume remains constant.


Given time the body will adapt to the high altitude conditions by increasing the number of red blood cells in the blood.  Back down at sea level your body would then be able to transport more oxygen and your performance would be enhanced.