Fill in the blanks
(a) The volume of a cube of side 1 cm is equal to …..m3
(b) The surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is equal to
…(mm)2
(c) A vehicle moving with a speed of 18 km h–1 covers….m in 1 s
(d) The relative density of lead is 11.3. Its density is ….g cm–3 or ….kg m–3
.
Fill in the blanks by suitable conversion of units
(a) 1 kg m2
s–2 = ….g cm2 s
–2
(b) 1 m = ….. ly
(c) 3.0 m s–2 = …. km h–2
(d) G = 6.67 × 10–11 N m2
(kg)–2 = …. (cm)3
s–2 g–1
.
A calorie is a unit of heat (energy in transit) and it equals about 4.2 J where 1J =
1 kg m2
s–2. Suppose we employ a system of units in which the unit of mass equals α
kg, the unit of length equals β m, the unit of time is γ s. Show that a calorie has a
magnitude 4.2 α
–1 β
–2 γ
2
in terms of the new units.
Explain this statement clearly :
“To call a dimensional quantity ‘large’ or ‘small’ is meaningless without specifying a
standard for comparison”. In view of this, reframe the following statements wherever
necessary :
(a) atoms are very small objects
(b) a jet plane moves with great speed
(c) the mass of Jupiter is very large
(d) the air inside this room contains a large number of molecules
(e) a proton is much more massive than an electron
(f) the speed of sound is much smaller than the speed of light.
The Sun is a hot plasma (ionized matter) with its inner core at a temperature exceeding
107 K, and its outer surface at a temperature of about 6000 K. At these high
temperatures, no substance remains in a solid or liquid phase. In what range do you
expect the mass density of the Sun to be, in the range of densities of solids and
liquids or gases ? Check if your guess is correct from the following data : mass of the
Sun = 2.0 ×1030 kg, radius of the Sun = 7.0 × 108
m.
The Sun is a hot plasma (ionized matter) with its inner core at a temperature exceeding
107 K, and its outer surface at a temperature of about 6000 K. At these high
temperatures, no substance remains in a solid or liquid phase. In what range do you
expect the mass density of the Sun to be, in the range of densities of solids and
liquids or gases ? Check if your guess is correct from the following data : mass of the
Sun = 2.0 ×1030 kg, radius of the Sun = 7.0 × 108
m.
Explain this common observation clearly : If you look out of the window of a fast
moving train, the nearby trees, houses etc. seem to move rapidly in a direction opposite
to the train’s motion, but the distant objects (hill tops, the Moon, the stars etc.)
seem to be stationary. (In fact, since you are aware that you are moving, these
distant objects seem to move with you).
One mole of an ideal gas at standard temperature and pressure occupies 22.4 L
(molar volume). What is the ratio of molar volume to the atomic volume of a mole of
hydrogen ? (Take the size of hydrogen molecule to be about 1 Å). Why is this ratio
so large ?
The unit of length convenient on the atomic scale is known as an angstrom and is
denoted by Å: 1 Å = 10–10 m. The size of a hydrogen atom is about 0.5 Å. What is the
total atomic volume in m3
of a mole of hydrogen atoms ?
A famous relation in physics relates ‘moving mass’ m to the ‘rest mass’ mo
of a
particle in terms of its speed v and the speed of light, c. (This relation first arose as
a consequence of special relativity due to Albert Einstein). A boy recalls the relation
almost correctly but forgets where to put the constant c. He writes :
( )
m
m
1 v
0
=
−
2
1/2
.
Guess where to put the missing c.
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