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# NCERT solutions Physics Class 11 Part 1 chapter 2 Units and Measurements

## Chapter 2 - Units and Measurements

#### Pages 35 - 38

Fill in the blanks

The volume of a cube of side 1 cm is equal to.....m3

Q 1.1 | Page 35

Fill in the blanks

The surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is equal to ... (mm)2

Q 1.2 | Page 35

A vehicle moving with a speed of 18 km h–1covers....m in 1 s

Q 1.3 | Page 35

Fill in the blanks :-

The relative density of lead is 11.3. Its density is ....g cm–3or . ...kg m–3.

Q 1.4 | Page 35

Fill in the blanks by suitable conversion of units: 1 kg m2s–2= ....g cm2 s–2

Q 2.1 | Page 35

Fill in the blanks by suitable conversion of units:

3.0 m s–2=.... km h–2

Q 2.3 | Page 35

Fill in the blanks by suitable conversion of units:

G= 6.67 × 10–11 N m2 (kg)–2=.... (cm)3s–2 g–1.

Q 2.4 | Page 35

A calorie is a unit of heat or energy and it equals about 4.2 J where 1J = 1 kg m2s–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 γin terms of the new units.

Q 3 | Page 35

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.

Q 4 | Page 35

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?

Q 5 | Page 35

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 ?

Q 6 | Page 35

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?

Q 7 | Page 35

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

Q 8.1 | Page 35

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?

Q 8.2 | Page 35

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?

Q 8.3 | Page 35

The photograph of a house occupies an area of 1.75 cm2on a 35 mm slide. The slide is projected on to a screen, and the area of the house on the screen is 1.55 m2. What is the linear magnification of the projector-screen arrangement?

Q 9 | Page 35

State the number of significant figures in the following

0.007 m2

Q 10.1 | Page 35

State the number of significant figures in the following

0.2370 g cm–3

Q 10.3 | Page 35

State the number of significant figures in the following:

6.320 J

Q 10.4 | Page 35

State the number of significant figures in the following:

6.032 N m–2

Q 10.5 | Page 35

State the number of significant figures in the following:

0.0006032 m2

Q 10.6 | Page 35

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.

Q 11 | Page 36

The mass of a box measured by a grocer’s 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?

Q 12 | Page 36

A physical quantity is related to four observables a, b, c and as follows:

P=(a^3b^2)/((sqrtcd))

The percentage errors of measurement in aband d are 1%, 3%, 4% and 2%, respectively. What is the percentage error in the quantity P? If the value of calculated using the above relation turns out to be 3.763, to what value should you round off the result?

Q 13 | Page 36

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 (2pit)/T

(b) y = a sin vt

(c) y = (a/T) sin  t/a

d) y = (a/sqrt2) (sin 2πt / T + cos 2πt / 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.

Q 14 | Page 36

A famous relation in physics relates ‘moving mass’ to the ‘rest mass’ m0 of a particle in terms of its speed 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_0/(1-v^2)^(1/2)

Guess where to put the missing c.

Q 15 | Page 36

The unit of length convenient on the atomic scale is known as an angstrom and is denoted by Å: 1Å = 10^(-10)m . The size of a hydrogen atom is about 0.5Å. what is the total atomic volume in m3 of a mole of hydrogen atoms?

Q 16 | Page 36

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 1Å). Why is this ratio so large?

Q 17 | Page 36

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)

Q 18 | Page 36

The principle of ‘parallax’ in section 2.3.1 is used in the determination of distances of very distant stars. The baseline AB is the line joining the Earth’s two locations six months apart in its orbit around the Sun. That is, the baseline is about the diameter of the Earth’s orbit ≈ 3 × 1011m. However, even the nearest stars are so distant that with such a long baseline, they show parallax only of the order of 1” (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 1” (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 meters?

Q 19 | Page 36

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.

Q 21 | Page 37

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):

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

Q 22.1 | Page 37

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):

Q 22.2 | Page 37

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):-

the wind speed during a storm

Q 22.3 | Page 37

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):

Q 22.4 | Page 37

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):-

the number of air molecules in your classroom.

Q 22.5 | Page 37

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.

Q 23 | Page 37

When the planet Jupiter is at a distance of 824.7 million kilometres from the Earth, its angular diameter is measured to be 35.72″ of arc. Calculate the diameter of Jupiter

Q 24 | Page 37

A man walking briskly in rain with speed must slant his umbrella forward making an angle θ with the vertical. A student derives the following relation between θ and v: tan θ = v and checks that the relation has a correct limit: as v →0, θ → 0, 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.

Q 25 | Page 37

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?

Q 26 | Page 37

Estimate the average mass density of a sodium atom assuming its size to be about 2.5 Å. (Use the known values of Avogadro’s number and the atomic mass of sodium). Compare it with the density of sodium in its crystalline phase: 970 kg m–3. Are the two densities of the same order of magnitude? If so, why?

Q 27 | Page 37

The unit of length convenient on the nuclear scale is a fermi : 1 f = 10– 15 m. Nuclear sizes obey roughly the following empirical relation : r = r_0A^(1/3) where is the radius of the nucleus, its mass number, and ris 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

Q 28 | Page 37

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 to return after reflection at the Moon’s surface. How much is the radius of the lunar orbit around the Earth?

Q 29 | Page 37

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 s–1).

Q 30 | Page 38

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?

Q 31 | Page 38

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.

Q 32 | Page 38

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 (ce, 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?

Q 33 | Page 38

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