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

(^242) Aptitude Test Problems in Physics
quantity should be regarded as the final height of
the centre of mass of mercury. The initial position
of the centre of mass of mercury is obviously he =

118. Hence we can conclude that

A 2 = Mg ( — 8

l

) = Mgl,

where M = 21SpTer is the mass of mercury.

Finally, we o tain

5 °

7

A= A 1 + A

2

=—

2

p SI +—

4

p

me

rgS1 2 nt., 7.7 J.

2.40. The work A done by the external force as
a result of the application and subsequent removal
of the load is determined by the area ABCD of the
figure (see Fig. 69). According to the first law of
thermodynamics, the change in the internal energy
of the rod is equal to this work (the rod is thermally
insulated), i.e.

A W = A = kx 0 — x^0 ).

On the other hand, AW= C AT, where AT is the
change in the temperature of the rod, from which
we obtain

AT —

AW

—

Icx 0 (x —x^0 )

C C

2.41. Let the cylinder be filled with water to a

level x from the base. The change in buoyancy is

equal to the increase in the force of gravity acting

on the cylinder with water. Hence we may con-

clude that Ah = x. From the equilibrium con-

dition for the cylinder, we can write

paS = p 0 S + mg,

where pa is the gas pressure in the cylinder after

its filling with water, i.e. pa = p 0 mg/S. Using

Boyle's law, we can write pa (h — Ah) = pih,