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

(^256) Aptitude Test Problems in Physics
3.16. Let v^1 and v^2 be the velocities of the first and
second balls after the removal of the uniform elec-
tric field. By hypothesis, the angle between the
velocity vi and the initial velocity v is 60°. There-
fore, the change in the momentum of the first ball is
Apt = q1E At = miv sin 60°.
Here we use the condition that v 1 = v/2, which
implies that the change in the momentum AN
of the first ball occurs in a direction perpendicular
to the direction of its velocity vi.
Since E Api and the direction of variation
of the second ball momentum is parallel to the
direction of Api, we obtain for the velocity of the
second ball (it can easily be seen that the charges
on the balls have the same sign)
va --= u tan 30° = v
0 •
The corresponding change in the momentum
of the second ball is
may
Ap 2 =q 2 E At=
cos 30° '
Hence we obtain
m 1 sin 60° q 2 = 4 q
1=

4 ,

—

q 2 ma/cos 30° ' m 2 3 mi 3

3.17. The kinetic energy of the first ball released

at infinity (after a long time) can be determined

from the energy conservation law:

mut q2 1 _j_ 1

m ,

1

2 4ne 0 k al -r a 2 • • •^ a N-1^9

where a 1 , a 2 ,.. aN _I are the distances from

the first ball (before it was released) to the re-

maining balls in the circle, a 1 and aN _i being the

distances to the nearest neighbours, i.e. al =

61 , 7 _ 1 = a (N = 1977).