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**Exercise : ** Solutions of Questions on Page Number : **35**

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Q1 :
**
**

Fill in the blanks

(a) The volume of a cube of side 1 cm is equal
to.....m^{3}

(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}.

**Answer :**

(a) 1 cm =

Volume of the cube = 1 cm^{3}

But, 1 cm^{3} = 1 cm × 1
cm × 1 cm =

∴1 cm^{3} =
10^{â€“6} m^{3}

Hence, the volume of a cube of side 1 cm is equal to
10^{â€“6} m^{3}.

(b) The total surface area of a cylinder of radius *r* and
height *h* is

*S* = 2π*r* (*r* +
*h*).

Given that,

*r* = 2 cm = 2 × 1 cm = 2
× 10 mm = 20 mm

*h* = 10 cm = 10 × 10 mm =
100 mm

= 15072 = 1.5
× 10^{4} mm^{2}

(c) Using the conversion,

1 km/h =

Therefore, distance can be obtained using the relation:

Distance = Speed × Time = 5 × 1 = 5 m

Hence, the vehicle covers 5 m in 1 s.

(d) Relative density of a substance is given by the relation,

Relative density =

Density of water = 1 g/cm^{3}

Again, 1g =

1 cm^{3} =
10^{â€“6}
m^{3}

1 g/cm^{3} =

∴ 11.3 g/cm^{3} =
11.3 × 10^{3}
kg/m^{3}

Answer needs Correction? Click Here

Q2 :
**
**

Fill in the blanks by suitable conversion of units:

(a) 1 kg
m^{2}s^{-2}=
....g
cm^{2}s^{-2}

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

(c) 3.0 m
s^{-2}=....
km h^{-2}

(d) G= 6.67 x
10^{-11} N m^{2}
(kg)^{-2}=....
(cm)^{3}s^{-2}
g^{-1}.

**Answer :**

(a) 1 kg = 10^{3} g

1 m^{2} = 10^{4} cm^{2}

1 kg m^{2} s^{â€“2} = 1 kg
× 1 m^{2}
× 1
s^{â€“2}

=10^{3} g × 10^{4}
cm^{2} × 1
s^{â€“2} = 10^{7} g
cm^{2} s^{â€“2}

(b) Light year is the total distance travelled by light in one year.

1 ly = Speed of light × One year

= (3 × 10^{8} m/s)
× (365
× 24
× 60
× 60 s)

= 9.46 × 10^{15} m

(c) 1 m = 10^{â€“3} km

Again, 1 s =

1 s^{â€“1} = 3600
h^{â€“1}

1 s^{â€“2} = (3600)^{2}
h^{â€“2}

∴3 m
s^{â€“2} = (3
×
10^{â€“3} km)
× ((3600)^{2}
h^{â€“2}) = 3.88
× 10^{4} km
h^{â€“2}

(d) 1 N = 1 kg m s^{â€“2}

1 kg = 10^{â€“3}
g^{â€“1}

1 m^{3} = 10^{6} cm^{3}

∴ 6.67
×
10^{â€“11} N m^{2}
kg^{â€“2} = 6.67
×
10^{â€“11}
× (1 kg m
s^{â€“2}) (1 m^{2}) (1
s^{â€“2})

= 6.67 ×
10^{â€“11}
× (1 kg
× 1 m^{3}
× 1
s^{â€“2})

= 6.67 ×
10^{â€“11}
×
(10^{â€“3}
g^{â€“1})
× (10^{6} cm^{3})
× (1
s^{â€“2})

= 6.67 ×
10^{â€“8} cm^{3}
s^{â€“2}
g^{â€“1}

Answer needs Correction? Click Here

Q3 :
**
**

A calorie is a unit of heat or energy and it equals about 4.2 J
where 1J = 1 kg m^{2}s^{-2}.
Suppose we employ a system of units in which the unit of mass
equals α kg, the unit of length
equals ÃŽÂ² m, the unit of time is
ÃŽÂ³ s. Show that a calorie has a
magnitude 4.2
α^{-1}
ÃŽÂ²^{-2}
ÃŽÂ³^{2} in terms of the new
units.

**Answer :**

Q4 :
**
**

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.

**Answer :**

Q5 :
**
**

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?

**Answer :**

Q6 :
**
**

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 ?

**Answer :**

Q7 :
**
**

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?

**Answer :**

Q8 :
**
**

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?

**Answer :**

Q9 :
**
**

The photograph of a house occupies an area of 1.75
cm^{2}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?

**Answer :**

Q10 :
**
**

State the number of significant figures in the following:

(a) 0.007 m^{2}

(b) 2.64 x
10^{24} kg

(c) 0.2370 g
cm^{-3}

(d) 6.320 J

(e) 6.032 N
m^{-2}

(f) 0.0006032 m^{2}

**Answer :**

Q11 :
**
**

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.

**Answer :**

Q12 :
**
**

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?

**Answer :**

Q13 :
**
**

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

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?

**Answer :**

Q14 :
**
**

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

(a)

(b) *y* = *a* sin *vt*

(c)

(d)

(*a* = maximum displacement of the particle, *v* =
speed of the particle. *T* = time-period of motion). Rule
out the wrong formulas on dimensional grounds.

**Answer :**

Q15 :
**
**

A famous relation in physics relates
'moving
mass'
*m* to the
'rest
mass'
*m*_{0} 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:

**Answer :**

Q16 :
**
**

The unit of length convenient on the atomic scale is known as an
angstrom and is denoted by. The size of a
hydrogen atom is aboutwhat is the total atomic
volume in m^{3} of a mole of hydrogen atoms?

**Answer :**

Q17 :
**
**

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). Why is this ratio so large?

**Answer :**

Q18 :
**
**

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).

**Answer :**

Q19 :
**
**

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
Ã¢â€°Ë† 3
x 10^{11}m. 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?

**Answer :**

Q20 :
**
**

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?

**Answer :**

Q21 :
**
**

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.

**Answer :**

Q22 :
**
**

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.

**Answer :**

Q23 :
**
**

The Sun is a hot plasma (ionized matter) with its inner
core at a temperature exceeding
10^{7} 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
** x **
10^{30} kg, radius of the
Sun = 7.0 ** x **
10^{8} m.

**Answer :**

Q24 :
**
**

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

**Answer :**

Q25 :
**
**

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

**Answer :**

Q26 :
**
**

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?

**Answer :**

Q27 :
**
**

Estimate the average mass density of a sodium atom assuming its
size to be about 2.5. (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^{â€“3}. Are the two densities of the
same order of magnitude? If so, why?

**Answer :**

Q28 :
**
**

The unit of length convenient on the nuclear scale is a
fermi : 1 f = 10^{â€“
15} m. Nuclear sizes obey roughly the following
empirical relation :

where *r* is the radius of
the nucleus, *A* its mass number,
and *r*_{0}
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.

**Answer :**

Q29 :
**
**

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?

**Answer :**

Q30 :
**
**

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}).

**Answer :**

Q31 :
**
**

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?

**Answer :**

Q32 :
**
**

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.

**Answer :**

Q33 :
**
**

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?

**Answer :**

Physics Part-1 - Physics : CBSE ** NCERT ** Exercise Solutions for Class 11th for ** Units And Measurements ** will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

- Physics Part-1 : Chapter 3 - Motion In A Plane Class 11
- Physics Part-1 : Chapter 2 - Motion In A Straight Line Class 11
- Physics Part-1 : Chapter 4 - Laws Of Motion Class 11
- Physics Part-2 : Chapter 1 - Mechanical Properties Of Solids Class 11
- Physics Part-1 : Chapter 7 - Gravitation Class 11
- Physics Part-1 : Chapter 5 - Work, Energy And Power Class 11
- Physics Part-2 : Chapter 7 - Waves Class 11
- Physics Part-1 : Chapter 6 - System Of Particles And Rotational Motion Class 11
- Physics Part-2 : Chapter 4 - Thermodynamics Class 11