1.290. What pressure has to be applied to the ends of a steel cyl-
inder to keep its length constant on raising its temperature by 100 °C?
1.291. What internal pressure (in the absence of an external pres-
sure) can be sustained
(a) by a glass tube; (b) by a glass spherical flask, if in both cases
the wall thickness is equal to Or = 1.0 mm and the radius of the
tube and the flask equals r = 25 mm?
1.292. A horizontally oriented copper rod of length
1 =
1.0 m
is rotated about a vertical axis passing through its middle. What
is the number of rps at which this rod ruptures?
1.293. A ring of radius r = 25 cm made of lead wire is rotated
about a stationary vertical axis passing through its centre and per-
pendicular to the plane of the ring. What is the number of rps at
which the ring ruptures?
1.294. A steel wire of diameter
d =
1.0 mm is stretched horizon-
tally between two clamps located at the distance
1 =
2.0 m from
each other. A weight of mass m = 0.25 kg is suspended from the mid-
point
0
of the wire. What will the resulting descent of the point
0
be in centimetres?
1.295. A uniform elastic plank moves over a smooth horizontal
plane due to a constant force F
o
distributed uniformly over the end
face. The surface of the end face is equal to
S,
and Young's modulus
of the material to
E.
Find the compressive strain of the plank in the
direction of the acting force.
1.296. A thin uniform copper rod of length
1
and mass m rotates
uniformly with an angular velocity w in a horizontal plane about a
vertical axis passing through one of its ends. Determine the tension
in the rod as a function of the distance r from the rotation axis. Find
the elongation of the rod.
1.297. A solid copper cylinder of length
1 =
65 cm is placed on a
horizontal surface and subjected to a vertical compressive force
F =
1000 N directed downward and distributed uniformly over the
end face. What will be the resulting change of the volume of the
cylinder in cubic millimetres?
1.298. A copper rod of length
1
is suspended from the ceiling by one
of its ends. Find:
(a)
the elongation Al of the rod due to its own weight;
(b)
the relative increment of its volume AVIV.
1.299. A bar made of material whose Young's modulus is equal to
E
and Poisson's ratio to 11, is subjected to the hydrostatic pressure
p.
Find:
(a)
the fractional decrement of its volume;
(b)
the relationship between the compressibility
3
and the elastic
constants
E
and 1.1.
Show that Poisson's ratio IA cannot exceed 1/2.
1.300. One end of a steel rectangular girder is embedded into a
wall (Fig. 1.74). Due to gravity it sags slightly. Find the radius of
curvature of the neutral layer (see the dotted line in the figure) in
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