198 Aptitude Test Problems in Physicsupward uniformly accelerated motion to the period
T up:
tupCif) (^77) ip cc tuP
The time measured by the pendulum clock moving
downwards with the acceleration a is
tdown
tdown' (^) — tdown Vg- a•
By hypothesis, the times of the uniformly accel-
erated downward and upward motions are equal:
tdown tap = t1/ 2 , where t^1 is the total time of
accelerated motion of the lift. Therefore, the
time measured by the pendulum clock during a
working day is
, t 1 g -I- a
t -- 2 — g
Here to is the time
lift. The stationary
cate
t t 1 + to.
It can easily be seen that the inequality Vg + a +
— a <27rg is fulfilled. Indeed,
jig-Fal-Vg—a )2 g+ Vg2 a2
Hence it follows that on the average the pendulum
clock in the lift lags behind: t' < t, and hence the
operator works too much.
1.101. Pascal's law implies that the pressure of a
gas in communicating vessels is the same at the
same altitude. Since the tubes of the manometer
communicate with the atmosphere, the pressure
in them varies with altitude according to the same
law as the atmospheric air pressure. This means
that the pressure exerted by the air on the liquid
in different arms of the manometer is the same and
Tdown
r 0— a
+1/ )+tu.
of the uniform motion of the
pendulum clock would indi-
2
< 1.
lig. 2g