Detailed explanations in West Bengal Board Class 9 Physical Science Book Solutions Chapter 1 Measurement offer valuable context and analysis.

## WBBSE Class 9 Physical Science Chapter 1 Question Answer – Measurement

Very short answer type questions

Question 1.

What is a physical quantity ?

Answer:

A physical quantity is any measurable quantity of an object or an event.

Question 2.

For clear understanding what must be present in the result obtained after measuring a physical quantity ?

Answer:

Unit.

Question 3.

By which instrument we to measure the weight of a body ?

Answer:

Spring balance.

Question 4.

Is litre a fundamental unit or a derived unit ?

Answer:

Derived unit.

Question 5.

What is the unit of atomic weight ?

Answer:

No unit.

Question 6.

Is light-year a fundamental or a derived unit ?

Answer:

Fundamental unit.

Question 7.

How many fundamental physical quantities are present in the derived physical quantity momentum ?

Answer:

Three. They are Mass, Length, Time.

Question 8.

Is work done by a force a scalar or a vector quantity ?

Answer:

Scalar quantity.

Question 9.

Which unit should be chosen to measure the distance between two stars ?

Answer:

Light year.

Question 10.

What is the SI unit of temperature ?

Answer:

Kelvin.

Question 11.

Write down a physical quantity which has no unit ?

Answer:

Atomic weight.

Question 12.

What type of time measuring device is used in a race?

Answer:

Stop-watch.

Question 13.

Which physical quantity is measured by a common balance?

Answer:

Mass.

Question 14.

What is the type of unit of velocity ?

Answer:

Derived unit.

Question 15.

Whose unit is millilitre ?

Answer:

Volume.

Question 16.

What is the unit of length in SI system ?

Answer:

Metre.

Question 17.

Name one physical quantity whose unit is formed by using all the three fundamental units.

Answer:

Force.

Question 18.

Which instrument is usually used to measure length ?

Answer:

Ordinary scale.

Question 19.

What is the unit of density in SI system ?

Answer:

kg m^{3}.

Question 20.

What is the unit of volume in CGS system ?

Answer:

cm^{3}

Question 21.

Is unit of area a fundamental unit ?

Answer:

No.

Question 22.

How many seconds are there in a mean solar day ?

Answer:

86,400 seconds.

Question 23.

What must be mentioned in the result obtained after measuring a physical quantity apart from a number?

Answer:

Unit must be mentioned in the result.

Question 24.

Name two physical quantities having same unit ?

Answer:

Speed and velocity.

Question 25.

Why is the temperature 4°C mentioned in defining density of water inCGS system ?

Answer:

Because at 4°C, water has maximum density which is 1 c.c. and water has the mass 1g.

Question 26.

Arrange in ascending order of magnitude : 1 micron, 1 angstrom, 1 fermi.

Answer:

1 fermi < 1 angstrom < 1 micron.

Question 27.

What is the unit of refractive index?

Answer:

No unit.

Question 28.

Write down the SI unit of momentum.

Answer:

kg-m/sec

Question 29.

How many metre is one Fermi ?

Answer:

1 Fermi =10^{-15} m.

Question 30.

Give an example of a scalar quantity which is the product of two vector quantities.

Answer:

Work.

Question 31.

What is the dimention of force?

Answer:

[MLT^{-2}].

Question 32.

Name a physical quantity which has a unit but no dimension.

Answer:

Angle.

Question 33.

Which unit should be chosen to measure distance between two planets ?

Answer:

Light year.

Question 34.

Write down the dimension of density.

Answer:

[ML^{-3}].

Question 35.

Is the unit of volume a fundamental or a derived unit ?

Answer:

Derived unit.

Question 36.

Write down theCGS unit of pressure.

Answer:

dyne/cm^{2}.

Question 37.

What is the SI unit of mass ?

Answer:

Kilogram.

Question 38.

Give the name of two scalar quantities which have same unit.

Answer:

Work and energy. Both have SI unit Joule andCGS unit erg.

Question 39.

What is the mass of 1 ml water at 4°C ?

Answer:

1 g.

Question 40.

The density of Hg is 13.6 g cm^{3}. What is the density of Hg in SI system ?

Answer:

13600 kg m^{3}.

Question 41.

At which temperature water has maximum density ?

Answer:

4°C.

Question 42.

Where is chronometer used ?

Answer:

The mariners use the chronometer for finding out longitude of a plane.

Question 43.

What is the dimension of velocity ?

Answer:

[LT^{-1}]

Question 44.

What is the dimension of retardation ?

Answer:

[LT^{-2}]

Question 45.

Which physical quantity has the dimension [MLT^{-2}] ?

Answer:

Force.

Question 46.

What is the SI unit of Force ?

Answer:

Newton.

Question 47.

Which physical quantity is meåsured by spring balance?

Answer:

Weight.

Question 48.

Give an example of a vector quantity which is derived from only one fundamental unit.

Answer:

Displacement.

Question 49.

The word ‘Science’ has its origin in a Latin word. Name it.

Answer:

Scientia.

Question 50.

The word ‘physics’ comes from a Greek word. What is it ?

Answer:

Physis.

Question 51.

What is measured by astronomical units ?

Answer:

Is is used in measuring astronomical distances.

Question 52.

Is ‘par sec’ a unit of time?

Answer:

No. It is the distance at which an arc of length of 1 AU (Astronomical unit) subtends an angle of one second of an arc.

Question 53.

What is the dimension of area?

Answer:

Dimension : The dimensions of a physical quantity are expressed as the powers to which the fundamental units of mass, length and time are raised to obtain the derived unit of the quantity.

Question 54.

What do we measure with a measuring cylinder?

Answer:

A measuring cylinder is used for measuring the volume of a liquid.

Question 55.

Name the device used in measuring weight of a body.

Answer:

Spring balance.

Question 56.

What does a stop watch measure ?

Answer:

Small time interval is measured by stop watch.

Question 57.

What is the multiplicative factor micro (mu) ?

Answer:

10^{-6}.

Question 58.

What do we measure with a common balance ?

Answer:

We measure the mass of a body usually with a common balance.

Short Answers type Questions

Question 1.

What is the necessity of measurement of a physical quantity ?

Answer:

Necessity of measurement of a physical quantity.

Measurement of a physical quantity gives a clear idea about largeness or smallness of the quantity. Simple eye estimation does not give any exact size of the physical quantity. For this reason, measurement of a physical quantity is very important.

Question 2.

What is physical quantity?

Answer:

Physical quantity : Any measurable physical entity is known as physical quantity.

e.g. length, mass, time etc.

Question 3.

What is scalar quantity ?

Answer:

Scalar quantity : The physical quantity which has only magnitude but no direction is called scalar quantity.

e.g. length, area, volume, mass etc.

Question 4.

What do you mean by vector quantity?

Answer:

Vector quantity : The physical quantity which has both magnitude and direction is called vector quantity.

e.g. displacement, velocity, force, weight etc.

Question 5.

What is unit ?

Answer:

Unit : Unit is the universally accepted definite amount of a physical quantity taken as a standard for the measurement of the same physical quantity of any amount.

Question 6.

What are fundamental units ?

Answer:

Fundamental units : The units of physical quantities like length, mass and time which do not depend on each other and from which units of other physical quantities may be derived, are called fundamental units.

Question 7.

What are derived units ?

Answer:

Derived units : Those units which are derivable from one or more of the fundamental units are known as derived units.

e.g. units of acceleration, force, speed, momentum etc. are derived units.

Question 8.

Has every physical quantity a unit ?

Answer:

No, there are some physical quantities which are measured by the ratio of two identical quantities.

e.g. atomic weight, specific heat, specific gravity etc.

These physical quantities have no units, they are purely numerical numbers.

Question 9.

What are the characteristics of fundamental units ?

Answer:

Characteristics of fundamental units :

- They do not depend on each other.
- They can form the units of other physical quantities.
- They are only three in numbers.

Question 10.

What are the types of different system of units ?

Answer:

Different system of units : At present two different system of units are used in science throughout the world.

(a) CGS or Metric system.

(b) SI or international systems of units (1960).

Question 11.

What isCGS system ?

Answer:

CGS or French or Metric system : This system was originated in France but now it is used in the scientific measurements and is widely used throughout the world including India. From the initial letters of the words centimetre, gram and second, this system is calledCGS system. This is a decimal system.

Question 12.

What is SI unit ?

Answer:

SI or International System of units : In 1960, an international system of units of measurement known as SI system was recommended by the GeneralConference on Weights and Measures in order to have a consistent system of units and to simplify communications among the scientists.

Question 13.

Define metre.

Answer:

Metre : The distance between the two marks made on a platinum-iridium (90: 10) bar maintained at 0°C temperature preserved at International Bureau of Weights and Measures at Sevres near Paris considered as one metre (symbol : m).

Question 14.

What is the modern concept of metre ?

Answer:

Modern concept of metre (October, 1983) :

The distance travelled by light in \(\frac{1}{3 \times 10^8}\) sec. in vacuum is called 1 metre.

Question 15.

State different smaller units of length in SI system.

Answer:

Smaller units of length in SI system :

- Femtometre or Fermi (=10
^{-15} m)(fm)
- Picometre (=10
^{-1}2 m)(pm)
- X-ray unit (=10
^{-13} m)(Xu)
- Angstrom (=10
^{-1}0 m)(A°A)
- Nanometre (=10
^{-1}0 m)(nm)
- Micrometre or micron (=10
^{-6} m)
- Centimetre (=10
^{-2} m)(cm)
- Decimetre (=10
^{-1} m)(dm)

Question 16.

What are the bigger units of length ?

Answer:

Bigger units of length :

(i) Astronomical unit (AU): The average distance between the Earth and the Sun.

1 AU = 14.95 × 10^{8} km

(ii) Light year : The distance that light wave travels in year in vacuum.

1 light year = 9.46 × 10^{12} km

(iii) Persec : The biggest unit for the measurement of distance. 1 persec = 3.26 light year = 30.84 × 10^{12} km.

Question 17.

What do you mean by mass ?

Answer:

Mass : Mass of a body is the quantity of matter contained in it.

Question 18.

State the bigger units of mass.

Answer:

Bigger units of mass :

- Quintal (= 100 kg)
- Metric ton or tonne (= 1000 kg = 10 Quintal)
- CSL (= 1.4 × mass of the Sun)

Question 19.

State the smaller units of mass.

Answer:

Smaller units of mass :

(i) amu(= 1.6603 × 10^{-2}4g)

(ii) 1 carat = 200 mg

Question 20.

What is density ? State itsCGS and SI units.

Answer:

Density : Density of the material of a body is the quantity of its mass per unit volume.

Unit of density inCGS system : g cm^{-3}

Unit of density in SI system : kg m^{-3}

Question 21.

What is Solar day?

Answer:

Solar day : The interval of time between two consecutive apparent transits of the Sun across the meridian at any place is called a Solar day.

Question 22.

What do you mean by mean Solar day ?

Answer:

Mean Solar day : The length of the Solar day varies from day to day owing to various reasons and the mean value of the actual Solar days averaged over a full year is called the mean Solar day.

Question 23.

What is the definition of second in SI system ?

Answer:

Definition of second in SI system : The time taken for the number of vibrations 9,192,631,770 of a radioactive atom Cs^{133} in standard magnetic field is called one second.

Question 24.

What do you mean by volume?

Answer:

Volume : It is defined to be the space occupied by a substance. Solids have three dimensions i.e. length, breadth and height.

Question 25.

What is litre?

Answer:

Litre : Volume of 1 kg of pure water at 4°C or 277 K is called a litre.

Question 26.

What are the advantages of metric system ?

Answer:

Advantages of metric system :

- In metric system, multiples and sub-multiples of the units of length and mass are always ten times the preceding ones.
- In metric system, units of length, mass and volume are related by same relation.
- In metric system, the same prefixes (such as milli, centi, deci etc.) are used in the units of length and mass.

Question 27.

What is the definition of dimension ?

Answer:

Definition of dimension : Dimensions of a derived unit are the powers to which the fundamental units of mass, length and time must be raised to present that unit.

Question 28.

What is the definition of dimensional expression ?

Answer:

Definition of dimensional expression : Dimensional expression is a product or quotient of the symbols of fundamental physical quantities, involved in a derived physical quantity raised to appropriate powers.

e.g. Dimensional expression of force : [MLT^{-2}].

Question 29.

State physical quantities without dimension.

Answer:

Physical quantities without dimension : A physical quantity is expressed as a ratio between two physical quantities of same unit becomes a number only, which will not have dimension.

e.g. Mechanical advantage of a machine, specific gravity, refractive index etc. are dimensionless. Again, angle although has unit (radian), it has no dimension.

Question 30.

What is the function of ordinary scale ?

Answer:

Function of ordinary scale : We generally use ordinary scale for the measurement of length.

Question 31.

How can you measure the length of a curved line ?

Answer:

Measurement of the length of a curved line: If the length of a curved line is to be measured with the help of a scale, we make use of a thread and place it along the curved line and measure the length of the straightened thread with the help of a scale.

Question 32.

Why scales are made usually with wood or plastic ?

Answer:

Scales are made

usually with wood or plastic: In making an ordinary scale wood or plastic is usually used instead of metal with the change in atmospheric temperature metal scales change in length. A metal scale gives correct readings only at a temperature at which it has been graduated. At any other temperatures it would give incorrect measurements. But in the case of wood or plastic these changes are negligible. So the scales are made usually with wood or plastics.

Question 33.

What is common balance?

Answer:

Common balance : In the laboratory we measure the mass of a body with a common balance. The weighing balance used in our daily life is simple version of this common balance.

Question 34.

What is the working principle of measurement of mass ?

Answer:

Working principle of measurement of mass : Actually we find the mass of the body by comparing its mass with some standard weights. Generally the measurable object as kept on the left pan of the balance and the standard weights are placed on the right pan. When the balance beam is horizontal, then

Mass of the object = Mass of the Standard Weights

Question 35.

What are the requisites of a good balance?

Answer:

Requisites of a good balance :

- The balance must be true, i.e. the balance beam should be horizontal with no loads or with equal loads on the pans.
- The balance must be sensitive.
- The balance must be stable i.e. the balance beam must came quickly to its equilibrium position once it is displaced.
- The balance must be rigid i.e. all the parts of the balance must. be strongly built.

Question 36.

What is a sensitive balance ? What are the conditions to be a sensitive balance?

Answer:

Sensitive balance : A balance is said to be sensitive when even for slight difference in weights on the two pans, the beam should be tilted from its horizontal position.

Conditions for balance to be sensitive :

(i) The balance beam should be light with long arms.

(ii) The centre of gravity of the beam should be near the fulcrum.

Question 37.

What is spring balance?

Answer:

Spring balance: With the help of this instrument weight of a body can be measured.

Question 38.

What is the working principle of measurement of weight ?

Answer:

Working principle of measurement of weight : The spring balance should be kept vertical and the pointer should be coincide with the ‘0’ mark of the scale. When a weight is suspended from the hook, the spring elongates, elongation being proportional to the weight. So, the pointer attached to the spring moves over the graduated scale. By noting its position against the scale, we can directly measure the weight of a body.

Question 39.

What is measuring cylinder ?

Answer:

Measuring cylinder: The instrument by which the volume of a liquid is measured is known as measuring cylinder.

Question 40.

What points should be noted during measuring the volume of liquid?

Answer:

Points should be noted :

(i) The volume of a liquid cannot be measured by measuring cylinder which reacts with glass.

(ii) The volume of a liquid cannot be measured by cylinder which is very much volatile.

Question 41.

How can you measure the density of an irregularly shaped body by using common balance and measuring cylinder ?

Answer:

Density : Density of a substance is defined as mass per unit volume of the substance.

If M be the mass of the substance, V the volume, then the density D is given by D = MV

Mass of the irregularly shaped body is determined by a common balance and volume is measured by a measuring cylinder. From equation (1) density of the body can be determined.

Question 42.

How will you determine the volume of a solid by a measuring cylinder?

Answer:

Determination of the volume of a solid by a measuring cylinder: To find the volume of the solid, some liquid in which the solid sinks but does not dissolve is taken in a dry measuring cylinder. The reading of the upper meniscus of the liquid in the cylinder is noted, let it be V_{1} ml . The solid substance tied with a waxed thread is now slowly immersed in the liquid. Let the reading of the upper meniscus of the liquid in a measuring cylinder be V_{2} ml. So, the volume of the given solid is (V_{2}-V_{1}) ml.

Question 43.

What precautions should be taken while determining volume and density of a solid body with the help of a common balance?

Answer:

Precautions:

- The body must sink completely in the liquid taken in the measuring cylinder.
- The body must not react chemically with the liquid and also it must not dissolve in the liquid.
- While dipping the body in the liquid taken in measuring cylinder, it should be done carefully so that no liquid splashes out.

Question 44.

Is density of a material dependent on its mass or volume?

Answer:

Density of a substance is independent of its mass or volume. If the mass of a substance is increased or decreased, its volume correspondingly increases or decreases proportionately and vice versa. So, density, the ratio of mass to volume remains unaltered.

Question 45.

Why is temperature kept at 4°C is measuring the volume of a liquid in litre unit ?

Answer:

Density of pure water is maximum at 4°C and it varies with the change of temperature and so also the volume. Hence, temperature of 4°C is specified in litre unit.

Question 46.

Why one does not express his age in second?

Answer:

A person does not express his age in seconds, because with such a small unit of time the number expressing his age will be very large that gives no clear idea about the age. Above all, in calculating age in seconds and then expressing it with a large number, some more seconds will pass off which do not come into the calculation. So, the correct age of one cannot be expressed in seconds.

Broad answer type Questions

Question 1.

Distinguish between scalar and vector quantities.

Answer:

Difference between scalar and vector quantities :

Scalar guantity |
Vector quantity |

(i) Scalar quantities have only magnitude and no direction. |
(i) Vector quantities have both magnitude and direction. |

(ii) Scalar quantities change due to change of magnitude only. |
(ii) Vector quantities change due to change of magnitude or direction or both. |

(iii) So far as addition, subtraction, multiplication etc. are concerned, scalar quantities obey algebraic laws. |
(iii) So far as addition, subtraction multiplication etc. are concerned, vector quantities do not obey algebraic laws. |

Question 2.

Write down the names and symbols of the fundamental units in SI system.

Answer:

Various fundamental physical quantities in SI system :

Question 3.

What are the advantages of metric system ?

Answer:

Advantages of metric system :

(i) In metric system, multiples and sub-multiples of the units of length and mass are always ten times the preceding ones. Thus the system is known as decimal system.In this system conversion of different multiples and sub-multiples of the units could be done by shifting the decimal point to the right or left.

(ii) In metric system, units of length mass and volume are related by simple relation.

(iii) In metric system, the same prefixes (such as milli, centi, deci etc.) are used in the units of length and mass

Question 4.

Why is temperature mentioned in the unit of length but not in the unit of mass ?

Answer:

The length is measured by a scale made of metals, plastic, wood or Gutta-percha etc. The length of these substances vary with difference of temperature. So in determining the unit of length temperature is to be specified to get the exact length. On the other hand mass being on intrinsic property of matter it does not vary with the change of temperature. So it is not necessary to specify the temperature.

Question 5.

How can you measure the exact mass of a solid by a common batance with unequal arm length ?

Answer:

Suppose the length of left and right arm of the balance are l_{1} and l_{2} respectively.

Now, keeping the solid with a mass of in at the right hand pan it is counterpoised with a mass w_{1} at the left hand pan.

Now, w_{1} × l_{1} = m × l_{2}

or, \(\frac{l_1}{l_2}=\frac{m}{w_1}\) ….. …. (i)

Again, the solid of mass ‘m’ is kept at the left hand pan and supposed it is counterpoised with a load of mass w_{2} at the right hand pan.

Question 6.

How can you measure the diameter of a piece of hair or thread?

Answer:

Measurement the diameter of a piece of hair or thread : To find diameter of a piece of hair or thread, a long piece of hair or thread is taken. The piece is then coiled over the millimetre marks on the scale. The coiling should be such that each turn remains in close contact of its adjacent one. Thus the added diametre of the segments of hair or thread in all the turns cover a few millimetre of the scale which is noted. Now dividing the length covered by the turns of hair or thread on the scale by the number of turns, diameter of the hair or thread is determined.

Question 7.

In theasuring certain length with a ruier why different portions of the ruier are made co-incident with the two ends of the given length ?

Answer:

As the graduation marks on the scale may not be uniformly spaced, due to manufacturing defects, several portions of the scale should be used i.e. the left end of the line may be made co-incident with different arbitrarily chosen marks of the scale like, 43 cm mark, 5.1 cm mark, 7.2 cm mark etc. The average of the several readings obtained after the above mentioned operations gives the required length of the line almost correctly.

Question 8.

How can you find the radius of a drop of a liquid ?

Answer:

Decermination of the radius of a drop of a hiquid: In order to find the radius of a drop of a liquid, a large number, say 200 drops of the liquid are taken in a dry measuring cylinder of small diameter. The drops of the liquid are taken with the help of a burette. The volume of the liquid is observed from the measuring cylinder. Now, it is divided with the number of drops of liquid taken when the volume of one drop is determined, then v ml = \(\frac{4}{3}\) πr_{3}, where π = 3.14.

So, the radius of the drop of liquid is determined.

Numerical Problems

Working formula :

(i) Volume of a rectangle solid = length × breadth × height

= l × b × h

(ii) Volume of a cube =(length)_{3}=l_{3}

(iii) Volume of a sphere = \(\frac{4}{3}\) π(radius )_{3} = \(\frac{4}{3}\) πr_{3}

(iv) Volume of a cone = \(\frac{1}{3}\) π × (radius of base)^{2} × perpendicular height

= \(\frac{1}{3}\) πr^{2} h(π = \(\frac{22}{7}\))

(v) Volume of a right circular cylinder =πr^{2} h

(vi) Density of a substance (D) = \(\frac{\text { Mass of the substance }(M)}{\text { Volume of the substance }(V)}\)

Example 1 : The mass of a proton is 1.67 × 10-27 kg. How many protons would be required to make 1 kg ?

Answer:

Example 2: The radius of an atom is abon: 1 A while that of the nucleus is about 1 fermi. How does the volume of the atom compared with that of the nucleus of the atom:

Answer:

1A**°** = 10^{-1}0 m, 1 fermi = 10^{-1}5 m

So, from the problem we get,

Therefore, volume of the atom is 10^{15} times greater than that of the nucleus.

Example 3 : Light of a certain colour is composed of a train of waves, each of 0.3048 micron long. How mans of the are are there in a metre?

Answer:

1 micron =10^{-6} m

∴ Number of waves

Example 4 : Mankind has existed for about 106 years, whereas the universe is about 1010 years old. If the age of the universe is taken to be one day, for how many seconds has mankind existed?

Answer:

From the problem we get,

10^{10} years =24 × 60 × 60 sec.

Example 5 : Mass of a piece of gold in air is 193 g. In a measuring cylinder there is 50 cm 3 of water. When the piece of gold is immersed in water in the measuring cylinder, the reading of the volume of water is found to be 60 cm 3. What is the density of gold?

Answer:

From the problem we get, Volume of the piece of gold =(60-50) cm^{3}=10 cm^{3}

Example 6: If the mass and volume of a piece of iron be 760 g and 100 cm^{3}, then what would be its density?

Answer:

Density of iron = \(\frac{\text { mass of iron }}{\text { volume of iron }}\)

= \(\frac{760 \mathrm{~g}}{100 \mathrm{~cm}^3}\) = 7.6 g/cm^{3}

Example 7 : The volume of a can is 100 ml and it weighs 20 g. It is then filled fully by a liquid and weighs 180 g. Find the density of the liquid.

Answer: Volume of the liquid (v) = 100 ml

Mass of the liquid (M) = (180-20) g = 160 g

Example 8: The density of a liquid is 1.2 g / cm^{3}. What will be the mass of 100 cm^{3} of the liquid?

Answer: Volume of the liquid =100 cm^{3}

Density of the liquid =1.2 g / cm^{3}

We know,

Mass of liquid =volume of the liquid × density of the liquid

= (100 × 1.2)g = 120g

Example 9 : The density of silver in CGS unit is 10.5 g / cm^{3}. What will be the density of silver in SI unit?

Answer: From the problem we get, density of silver in CGS unit =10.5 g / cm^{3}

So, the density of silver in SI unit

= 10.5 × 1000 kg / m^{3}

= 10500 kg / m^{3}

Example 10: The radius of a solid sphere is 10 cm. The density of its matter is 8 g / cm 3. What is the mass of the sphere?

Answer:

We know,

volume of the sphere V = \(\frac{4}{3}\) πr^{3}(r= radius of the sphere)

∴ \(\frac{4}{3}\) × \(\frac{22}{7}\) × (10)^{3} cm^{3} ; r = 10cm

Density of its matter = 8 g/cm^{3}

So, mass of sphere = volume × density

= \(\frac{4}{3}\) × \(\frac{22}{7}\) ×(10)^{3} × 8g=33.51 kg

Example 11.

Mass of a piece of solid substance is 20.52 g. When the piece is immersed in water its mass becomes 12.48 g. What will be its volume and density?

Answer:

Mass of displaced water by the body =(20.52-12.48) g=8.04 g

Volume of displaced water = \(\frac{8 \cdot 04}{1 \mathrm{~g} / \mathrm{cc}}\) = 8.04 c.c.

So, the volume of the solid substance = 8.04 c.c.

Density = \(\frac{20 \cdot 52}{8 \cdot 04}\) g / c.c. =2.55 g / c.c.

Example 12.

Find the dimension of force.

Answer:

Example 13.

Specific gravity is the ratio of two densities. Show that it has no dimension.

Answer:

Specific gravity of a substance

So, specific gravity is dimensionless.

Example 14.

Kinetic energy is given by \(\frac{1}{2}\) mv 2 and potential energy by mgh. Show that both of them have same dimensions.

Answer:

Kinetic energy =\(\frac{1}{2}\) mv^{2}

= [M] ×[LT^{-1}]^{-2}=[ML^{2} T^{-2}]

Potential energy =mgh=[M] ×[LT^{-2}] ×[L]

= [ML^{2} T^{-2}]

So, kinetic and potential energies have same dimensions.

Example 15.

Find the dimension of power.

Answer:

Example 16.

In CGS system density of water is 1 g / cc. Find the density of water in SI unit.

Answer:

Density of water =1 g / cc

= 1 g / 1 cm^{3}

∴ Density of water in SI unit is 1000 kgm^{-3}.

Example 17 :

xpress a light year in megametre

Answer:

Light year is the distance travelled by the light in one year at the speed 3 × 10^{8} m / s.

One megametre =10^{6} m

∴ Distance travelled by light in one year (365 days)

= 94608 × 10^{5} Mm