Aptitude Test Problems in Physics Science for Everyone by S Krotov ( PDFDrive.com )

Solutions^193

1.95. The period of oscillations of the pendulum

in the direction perpendicular to the rails is

T 1 = 231/

T

-

7

g

(1 is the length of the weightless inextensible thread)

since the load M is at rest in this case (Fig. 188).

Fig._187 Fig. 188

The period of oscillations in the plane parallel
to the rails ("parallel" oscillations) can be found
from the condition that the centre of mass of the
system remains stationary. The position of the
centre:of mass of the system is determined from the
equation m1 1 = M (1 — 1 1 ). Thus, the ball per-
forms oscillations with point 0 remaining at rest
and is at a distance / 1 = Ml/(M m) from point

0. Hence the period of "parallel" oscillations of
   the pendulum is

Ml

T2

=2n v (ffi m) g

Consequently,

T2 (^) M
Ti m+M •
1.96. The force exerted by the rods on the load is
F 1 = 2Ften cos a, while the force exerted on the
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