NCERT Solutions Class 11 Physics Chapter 2 Units And Measurement Download In Pdf

Chapter 2 Units And Measurement Download in pdf

**Question 2. 1 **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 hâ1 covers....m in 1 s

(d) The relative density of lead is 11.3. Its density is ....g cmâ3 or ....kg mâ3.

**Question 2. 2 **Fill in the blanks by suitable conversion of units

(a) 1 kg m2 sâ2 = ....g cm2 sâ2

(b) 1 m = ..... ly

(c) 3.0 m sâ2 = .... km hâ2

(d) G = 6.67 Ă 10â11 N m2 (kg)â2 = .... (cm)3 sâ2 gâ1.

**Question 2. 3 **A calorie is a unit of heat or energy and it equals about 4.2 J where 1J = 1 kg m2 sâ2. Suppose we employ a system of units in which the unit of mass equals Îą kg, the unit
of length equals Î˛ m, the unit of time is Îł s. Show that a calorie has a magnitude 4.2
Îąâ1 Î˛ â2 Îł 2 in terms of the new units.

**Question 2. 4** Explain this statement clearly :
âTo call a dimensional quantity âlargeâ or âsmallâ is meaningless without specifying a
standard for comparisonâ. 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.

**Question 2. 5** A new unit of length is chosen such that the speed of light in vacuum is unity. What
is the distance between the Sun and the Earth in terms of the new unit if light takes
8 min and 20 s to cover this distance ?

**Question 2. 6 **Which of the following is the most precise device for measuring length :

(a) a vernier callipers with 20 divisions on the sliding scale

(b) a screw gauge of pitch 1 mm and 100 divisions on the circular scale

(c) an optical instrument that can measure length to within a wavelength of light ?

**Question 2. 7** A student measures the thickness of a human hair by looking at it through a
microscope of magnification 100. He makes 20 observations and finds that the average
width of the hair in the field of view of the microscope is 3.5 mm. What is the
estimate on the thickness of hair ?

**Question 2. 8** Answer the following :

(a)You are given a thread and a metre scale. How will you estimate the diameter of
the thread ?

(b)A screw gauge has a pitch of 1.0 mm and 200 divisions on the circular scale. Do
you think it is possible to increase the accuracy of the screw gauge arbitrarily by
increasing the number of divisions on the circular scale ?

(c) The mean diameter of a thin brass rod is to be measured by vernier callipers. Why
is a set of 100 measurements of the diameter expected to yield a more reliable
estimate than a set of 5 measurements only ?

**Question 2. 9** The photograph of a house occupies an area of 1.75 cm2 on a 35 mm slide. The slide
is projected on to a screen, and the area of the house on the screen is 1.55 m 2. What
is the linear magnification of the projector-screen arrangement.
2.10 State the number of significant figures in the following :

(a) 0.007 m2

(b) 2. 64 Ă 1024 kg

(c) 0.2370 g cmâ3

(d) 6.320 J

(e) 6.032 N mâ2

(f) 0.0006032 m2

**Question 2. 11** The length, breadth and thickness of a rectangular sheet of metal are 4.234 m, 1.005 m,
and 2. 01 cm respectively. Give the area and volume of the sheet to correct significant
figures.

**Question 2. 12** The mass of a box measured by a grocerâs balance is 2. 300 kg. Two gold pieces of
masses 20.15 g and 20.17 g are added to the box. What is (a) the total mass of the
box, (b) the difference in the masses of the pieces to correct significant figures ?

**Question 2. 13 **A physical quantity P is related to four observables a, b, c and d as follows :
P = a3b2/ ( c d )
The percentage errors of measurement in a, b, c and d are 1%, 3%, 4% and 2%,
respectively. What is the percentage error in the quantity P ? If the value of P calculated
using the above relation turns out to be 3.763, to what value should you round off
the result ?

**Question 2. 14** A book with many printing errors contains four different formulas for the displacement
y of a particle undergoing a certain periodic motion :

(a) y = a sin 2Ď t/T

(b) y = a sin vt

(c) y = (a/T) sin t/a

(d) y = (a 2) (sin 2Ďt / T + cos 2Ďt / T )
(a = maximum displacement of the particle, v = speed of the particle. T = time-period
of motion). Rule out the wrong formulas on dimensional grounds.

**Question 2. 15** A famous relation in physics relates âmoving massâ m to the ârest massâ 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
â 2 1/2.
Guess where to put the missing c.

**Question 2. 16** The unit of length convenient on the atomic scale is known as an angstrom and is
denoted by Ă
: 1 Ă
= 10â10 m. The size of a hydrogen atom is about 0.5 Ă
. What is the
total atomic volume in m3 of a mole of hydrogen atoms ?

**Question 2. 17 **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 Ă
). Why is this ratio
so large ?

**Question 2. 18** 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 trainâs 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).

**Question 2. 19 **The principle of âparallaxâ in section 2.3.1 is used in the determination of distances
of very distant stars. The baseline AB is the line joining the Earthâs two locations six
months apart in its orbit around the Sun. That is, the baseline is about the diameter
of the Earthâs orbit â 3 Ă 1011m. However, even the nearest stars are so distant that
with such a long baseline, they show parallax only of the order of 1â (second) of arc
or so. A parsec is a convenient unit of length on the astronomical scale. It is the
distance of an object that will show a parallax of 1â (second) of arc from opposite
ends of a baseline equal to the distance from the Earth to the Sun. How much is a
parsec in terms of metres ?

**Question 2. 20** The nearest star to our solar system is 4.29 light years away. How much is this
distance in terms of parsecs? How much parallax would this star (named Alpha
Centauri) show when viewed from two locations of the Earth six months apart in its
orbit around the Sun ?

**Question 2. 21** Precise measurements of physical quantities are a need of science. For example, to
ascertain the speed of an aircraft, one must have an accurate method to find its
positions at closely separated instants of time. This was the actual motivation behind
the discovery of radar in World War II. Think of different examples in modern science
where precise measurements of length, time, mass etc. are needed. Also, wherever
you can, give a quantitative idea of the precision needed.

**Question 2. 22** Just as precise measurements are necessary in science, it is equally important to be
able to make rough estimates of quantities using rudimentary ideas and common
observations. Think of ways by which you can estimate the following (where an
estimate is difficult to obtain, try to get an upper bound on the quantity) :

(a) the total mass of rain-bearing clouds over India during the Monsoon

(b) the mass of an elephant

(c) the wind speed during a storm

(d) the number of strands of hair on your head

(e) the number of air molecules in your classroom.

**Question 2. 23** 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 Ă 1030 kg, radius of the Sun = 7.0 Ă 108 m.

**Question 2. 24** When the planet Jupiter is at a distance of 824.7 million kilometers from the Earth,
its angular diameter is measured to be 35.72â of arc. Calculate the diameter of
Jupiter.
Additional Exercises

**Question 2. 25** A man walking briskly in rain with speed v must slant his umbrella forward making
an angle Î¸ with the vertical. A student derives the following relation between Î¸ and
v : tan Î¸ = v and checks that the relation has a correct limit: as v â 0, Î¸ â0, as
expected. (We are assuming there is no strong wind and that the rain falls vertically
for a stationary man). Do you think this relation can be correct ? If not, guess the
correct relation.

**Question 2. 26** It is claimed that two cesium clocks, if allowed to run for 100 years, free from any
disturbance, may differ by only about 0.02 s. What does this imply for the accuracy
of the standard cesium clock in measuring a time-interval of 1 s ?

**Question 2. 27 **Estimate the average mass density of a sodium atom assuming its size to be about 2. 5 Ă
. (Use the known values of Avogadroâs number and the atomic mass of sodium).
Compare it with the density of sodium in its crystalline phase :

970 kg mâ3. Are the two densities of the same order of magnitude ? If so, why ?

**Question 2. 28 **The unit of length convenient on the nuclear scale is a fermi : 1 f = 10â15 m. Nuclear
sizes obey roughly the following empirical relation :
r = r0 A1/3
where r is the radius of the nucleus, A its mass number, and ro is a constant equal to
about, 1.2 f. Show that the rule implies that nuclear mass density is nearly constant
for different nuclei. Estimate the mass density of sodium nucleus. Compare it with
the average mass density of a sodium atom obtained in Exercise. 2. 27.

**Question 2. 29 **A LASER is a source of very intense, monochromatic, and unidirectional beam of
light. These properties of a laser light can be exploited to measure long distances.
The distance of the Moon from the Earth has been already determined very precisely
using a laser as a source of light. A laser light beamed at the Moon takes 2. 56 s toreturn after reflection at the Moonâs surface. How much is the radius of the lunar
orbit around the Earth ?

**Question 2. 30 **A SONAR (sound navigation and ranging) uses ultrasonic waves to detect and locate
objects under water. In a submarine equipped with a SONAR the time delay between
generation of a probe wave and the reception of its echo after reflection from an
enemy submarine is found to be 77.0 s. What is the distance of the enemy submarine?
(Speed of sound in water = 1450 m sâ1).

**Question 2. 31** The farthest objects in our Universe discovered by modern astronomers are so distant
that light emitted by them takes billions of years to reach the Earth. These objects
(known as quasars) have many puzzling features, which have not yet been satisfactorily
explained. What is the distance in km of a quasar from which light takes 3.0 billion
years to reach us ?

**Question 2. 32 **It is a well known fact that during a total solar eclipse the disk of the moon almost
completely covers the disk of the Sun. From this fact and from the information you
can gather from examples 2. 3 and 2. 4, determine the approximate diameter of the
moon.

**Question 2. 33** A great physicist of this century (P.A.M. Dirac) loved playing with numerical values of
Fundamental constants of nature. This led him to an interesting observation. Dirac
found that from the basic constants of atomic physics (c, e, mass of electron, mass of
proton) and the gravitational constant G, he could arrive at a number with the
dimension of time. Further, it was a very large number, its magnitude being close to
the present estimate on the age of the universe (~15 billion years). From the table of
fundamental constants in this book, try to see if you too can construct this number
(or any other interesting number you can think of ). If its coincidence with the age of
the universe were significant, what would this imply for the constancy of fundamental
constants ?

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- Chapter 1 Physical World
- Chapter 2 Units And Measurement
- Chapter 3 Motion In A Straight Line
- Chapter 4 Motion In A Plane
- Chapter 5 Laws Of Motion
- Chapter 7 Systems of Particles and Rotational Motion
- Chapter 6 Work Energy and Power
- Chapter 8 Gravitation
- Chapter 9 Mechanical Properties Of Solids
- Chapter 10 Mechanical Properties Of Fluids
- Chapter 11 Thermal Properties of Matter
- Chapter 12 Thermodynamics
- Chapter 13 Kinetic Theory
- Chapter 14 Oscillations
- Chapter 15 Waves

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