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

Solutions 183

Here mN , mE, coN, WE, RN, and RE are the

masses, angular velocities, and orbital radii of Nep-

tune and the Earth respectively, and M is the

mass of the Sun. We now take into account the

relation between the angular velocity and the

period of revolution around the Sun:

2:rt

0)N=

TN

• 0)E= TE •

Here TN and TE are the periods of revolution of

Neptune and the Earth. As a result, we find that

the period of revolution of Neptune around the

Sun is

R1 3 , 1

T TB N 71 -r 165 years.

A similar result is obtained for elliptical orbits

from Kepler's third law.

Fig. 180

1.85. Let us consider two methods of solving this
problem.

1. The equilibrium conditions for the loads
   have the form (Fig. 180)
   ma, T 2 = m 2 g,
   Mg = Ti sin a 1 + T2 sin a 2 ,
   T cos al = T2 cos a2.