1.) A solid object weighs 19.74 N in air. When it is suspended from a scale and

Question

1.) A solid object weighs 19.74 N in air. When it is suspended from a scale and submerged in water, the scale reads 6.54 N.

2.) In scuba diving, a regulator is used so that the pressure of the air the diver breathes is close to that of the ambient water. A reckless swimmer decides to use a hose sticking out of the surface to breathe underwater while diving in a lake. When the air pressure in the lungs is at a pressure of around 0.115 atmospheres below the ambient pressure, lung injury may occur. Find the depth at which the swimmer would experience such a pressure differential.
(in m)

3.) Three equal point masses are placed in different configurations on a disk rotating around its center (see below).

Rank the options in order of increasing moment of inertia.

Explanation / Answer

1)   The buoyant force = difference in the readings = 19.74 - 6.54 = 13.2 N
and it is also = (water)*g*V
so the volume V of the object is 13.2 N/(1000kg/m^3*9.80m/s^2) = 1.35x10^-3 m^3
Now the density of the object = m/V = (w/g)/V = 19.74N/(9.80*1.35x10^-3) = 1492.06 kg/m^3

2)  P(atm) + (Density)gh = P(atm) + 0.115atm
(Density)gh = 0.115atm
h = 0.115atm/(Density)(g)
Where P is the pressure in Atmospheres, Density is the density of the fluid, g is the acceleration due to gravity, and h is height below the surface.

h = 11652.375 Pa/(1000*9.8) = 1.19 m

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