Solutions (^201)
force of pressure exerted by water on the upper
strip is
[p — pw g (r + a)] AS,
while the force of pressure on the lower strip is
[p — pw g (r — a)] AS,
where AS is the area of a strip. The sum of these
forces is proportional to the area of the strip, the
proportionality factor 2 (p — pgr) being indepen-
dent of a. Hence it follows that the total force of
pressure of water on the piston is
(p — pw gr)nr 2 = [po pw g (h. — r)] nr 2.
The piston is in equilibrium when this force is equal
to the force of atmospheric pressure acting on the
piston from the left and equal to ponr 2. Hence
h=r,
i.e. the piston is in equilibrium when the level of
water in the vertical cylinder is equal to the ra-
dius of the horizontal cylinder. An analysis of the
solution shows that this. equilibrium is stable.
1.104. The condition of complete submergence of
a body is
M > pwV,
where M is the mass of the body, and V is its vol-
ume. In the case under consideration, we have
M= mcork mal, V-
mcork mal
Pcork^ Pal
Hence it follows that the minimum mass of the
wire is
Pal (P‘v —Pcork)
mal mcork^1.^6 mcork-
(Pal Pw) Pcork
1.105. Obviously, in equilibrium, the sphere is at
a certain height h above the bottom of the reser-
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