208 Aptitude Test Problems in Physics
we obtain the angular velocity of the tube:
- =
V (^2) P2—P1
Pw 1-4 •
1.115. Let the exponent a be such that the body
having an initial velocity u traverses a finite dis-
tance s (v) in the medium. Since the velocity of
the body monotonically decreases during its motion
in the medium, s (v) > s (v 1 ) for v > v 1. It is also
clear that s (v) tends to zero as v -4- 0. The con-
dition under which the body comes to a halt is
that the work A of the drag is equal to the initial
kinetic energy of the body:
mv 2
— A. (1)
2
Since the drag monotonically decreases with the
velocity of the body during its motion, we can
write
A 4. ttvc's (v). (2)
Substituting Eq. (2) into Eq. (1), we obtain
s in 2- v a
2p
whence it follows that for a „>..- 2, the condition
lim s (v) = 0 is violated. Therefore, for a > 2,
the body cannot be decelerated on the final region
of the path.
1.116. According to the law of universal gravi-
tation, the force of attraction of the body of mass m
to Mars on its surface is G —
M
2
m
—
m
, where MM is the
Rm
mass of Mars, and fim is its radius. This means
that the free-fall acceleration on the surface of
Mars is gm= GMmili►. If the mass of the Mar-
tian atmosphere is ?rim, it is attracted to the surface
of the planet with the force mmgm, which is equal