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

140 Aptitude Test Problems in Physics

The period of small (but still damped) oscillations

of the ball can be determined from the relation

2

T —

n

Vitt 11-p,2/(4m2)

2n

(g11) (^) + (μv/mg)'—R 2 /( 4 m')
1.39. We write the equilibrium condition for a
small segment of the string which had the length
Fig. 149
Ax before suspension and was at a distance x
from the point of suspension (Fig. 149):
Axg+T (x+ !ix). T (x),
where L is the length of the rubber string in the
unstretched state. Thus, it is clear that after the
suspension the tension will uniformly decrease
along the string from mg to zero.
Therefore, the elongations per unit length for
small equal segments of the string in the unstressed
state after the suspension will also linearly decrease
from the maximum value to zero. For this reason,
the half-sum of the elongations of two segments of
the string symmetric about its middle will be
equal to the elongation of the central segment which
experiences the tension mg/2. Consequently, the