Consider a simple
pendulum, having a bob attached to a
string, that oscillates under the action of
the force of gravity. Suppose that the period
of oscillation of the simple pendulum
depends on its length (l), mass of the bob
(m) and acceleration due to gravity (g).
Derive the expression for its time period
using method of dimensions.
Example 1.4 The SI unit of energy is
J = kg m2 s
–2; that of speed v is m s–1 and
of acceleration a is m s–2. Which of the
formulae for kinetic energy (K) given below
can you rule out on the basis of
dimensional arguments (m stands for the
mass of the body) :
(a) K = m2
v3
(b) K = (1/2)mv2
(c) K = ma
(d) K = (3/16)mv2
(e) K = (1/2)mv2 + ma
Let us consider an equation
1
2
m v m g h 2
=
where m is the mass of the body, v its
velocity, g is the acceleration due to
gravity and h is the height. Check
whether this equation is dimensionally
correct.
5.74 g of a substance
occupies 1.2 cm3
. Express its density by
keeping the significant figures in view.
Each side of a cube is
measured to be 7.203 m. What are the
total surface area and the volume of the
cube to appropriate significant figures?
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.
+91 94284 01196
© Copyright 2025. Doubtora. All Rights Reserved
