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Prof. Muhammad Amin 1
Chapter-1 measurement
Type equation here.
1.1 Name several repetitive phenomenon occurring in nature which could serve are
responsible time standards.
Ans. A natural phenomenon which repeats itself after equal intervals of time could be used as
time standard
e.g
The rotation of earth about its own axis and also around the sun.
The rotation of moon around the earth
Atomic vibrations in solid.
The change of shadow of an object in the sun.
1.2 Give the drawback to use the period of pendulum as time standard.
Ans. We know that the time period of pendulum is
2T = πg
The time period ‘T’ of a pendulum depends upon its length’ ’ and value of ‘g’. These
are following drawbacks to use the period of a pendulum as time standard.
Air resistance affect the time period.
The period of a pendulum varies with altitude because ‘g’ varies with altitude.
The effect of temperature on the length of pendulum.
1.3 Why do we find it useful to have two units for the amount of substance, the kilogram
and the mole?
Ans. Both kilogram and mole are S.I units of mass.
Kilogram is used for large mass when we require amount of substance without
considering number of atoms/molecules.
Mole is used for small mass when we require amount of substance by considering
number of atoms/molecules.
i.e 1 mole = 6.022 × 1023 atoms/molecules
1.4 The period of simple pendulum is measure by a stop watch. What type of errors are
possible in the time period?
Ans. The following errors are possible.
1. Random Error
Random error occurs when repeated measurements of a quantity give different values
under the same conditions.
It occurs due to some unknown reason
2. Systematic Error
Systematic error occurs due to the fault in the instrument. it always ocures under
some definite rule
e.g zero error, poor calibration
3. Personnel Error
Personal error occurs due to negligence or inexperience of a person.
Measurements Chapter
1
Important short questions
Prof. Muhammad Amin 2
Chapter-1 measurement
1.5 Does a dimensional analysis give any information of constant of proportionality that
may appear in an algebraic expression?
Ans. The dimensional analysis does not give any information about the constant of
proportionality, however, it can be found by experiments.
Example
F = 6 r V
Here 6 = constant of proportionality the numerical value of the constant cannot be
determined by dimensional analysis. However, it can be found by experiments.
1.6 Write the dimensions of (i) Pressure (ii) Density
Ans. (i) By definition,
Pressure = Force
Area
Dimension of pressure
F= P =
A
2
2
MLTP =
L
or 1 2P ML T
(ii) As density =Mass
Volume
Dimension of density
3
M
L
or 3ML
1.7 Write any three uses of dimensional analysis?
Ans: The use of dimensions is called dimensional analysis. The following are the main uses of
dimensional analysis.
(i) It is used to find the relationship between different physical quantities.
(ii) It is used to convert one system of unit into another.
(iii) It is used to confirm the correctness of any physical equation
1.8 Write any two drawbacks of dimensional analysis?
Ans: The following are the draw backs of dimensional analysis.
(i) The dimensional analysis is unable to find the values of various constants.
(ii) It cannot be applied to physical quantities involving trigonometric and logarithmic
functions.
(iii) It cannot differentiate between terms having same dimensions. For example work
and Torque, stress and pressure.
1.9 What is meant by S.I system?
Ans: in 1960, the internationally adopted system of units used by all the scientists and almost
all the countries of the world is international system (SI) of units. It consists of seven
base units, two supplementary units and a number of derived units.
Prof. Muhammad Amin 3
Chapter-1 measurement
The S.I base units
QUANTITIES
SYMBOL
OF
QUANTITY
UNIT
NAME
SYMBOL
OF UNIT
Length L Meter m.
Mass M Kilogram Kg.
Time T Second S.
Electric
Current I Ampere A.
Temperature T Kelvin K.
Light
Intensity L Candela Cd.
Amount of
Substance N Mole mol.
1.10 Differentiate b/w radian and steradian?
Ans: Radian
It is unit of plane angle made at the centre of a circle by an arc
equal in length to the radius of the circle.
If Arc AB = r, then
< AOB = 1 Radian
Steradian
The solid angle made at the centre of a sphere by its surface of
urea equal to square of its radius, is called Steradian.
1.11 State the principle of homogeneity of dimensions.
Ans: In order to check the correctness of an equation, we have to show
that the dimensions of the quantities on both sides of the equation are the same,
irrespectively of the form of formula. This is called the principle of homogeneity of
dimensions.
e.g E = mc2 is dimensionally consistent since dimensions of both sides are equal
i.e [L.H.S] = [R.H.S]
[ML2T-2] = [ML2T-2]
1.12 Define the types of error and their remedy (correction).
Ans: The errors in any measurement are usually classified into two types.
(i) Random Errors
Random error occurs when repeated measurements of a quantity give different
values under the same conditions.
Cause: It occurs due to some unknown reason.
Remedy:
Random error can be reduced by taken average of several readings.
(ii) Systematic Errors
Systematic error occurs due to the fault in the instrument. It always occurs under
some definite rule
Cause: zero error, poor calibration
Prof. Muhammad Amin 4
Chapter-1 measurement
Remedy:
Systematic error can be removed by comparing the faulty apparatus with a standard.
1.13 Differentiate between precision and accuracy.
Ans: A precise measurement is the one which has less absolute uncertainty and an accurate
measurement is the one which has less fractional or percentage uncertainty or error.
1.14 Calculate the dimensions of pressure and work?
Ans: Dimensions of Pressure
F
P Dimensionof work W F dA
2
2 2
maW MLT L
A
W ML T
2
2
MLT
L
1 2P ML T
1.15 Distinguish between base units and derived units?
Ans:
Base Units Derived Unit
Those units which cannot be defined in
terms of any other units known as base
units.
e.g These are units of base quantities.
kilogram, meter, second etc.
The units of the physical quantities
defined in terms of base and
supplementary units are known as
derived units.
e.g These are units of derived
quantities.
Newton, m/s , Pascal etc.
Prof. Muhammad Amin 5
Chapter-1 measurement
1.1 A light year is the distance light travels in one year. How many meters are there in one light
year: (speed of light = 3.0x 08 ms-1).
Solution:
Data:
Time = t = 1 year = 365 days
t = 365 x 24 x 60 x 60 sec
t = 31536000 s
Speed of light = c = 3.0 x 108 ms-1
To Find:
Distance = S =?
Calculation:
We know that
S = v t
v = c
S = ct
Putting the values, we get
S = 3 x 108 x 31536000
or 15S = 9.5 × 10 m Ans.
Conclusion:- There are 9.5 x 1015 meters in one light year
1.2 a) How many seconds are there in 1 year?
b) How many nanoseconds in 1 year?
c) How many years in 1 second?
To find
(a) Seconds in one year =?
(b) Nanoseconds in one year =?
(c) Years in one second =?
Solution:
(a) We already know that
1 year = 365 days
1 day = 24 hours
1 hour = 60 minutes
1 minute = 60 seconds
Therefore,
1 year = 365 x 24 x 60 x 60 sec
= 31536000 s
= 3.1536 x 107 s Ans
(b) As we know that
One year = 3.1536 x 107s
One second = 109 nanosecond (:1 nanosecond = 10-9s)
One year = 3.1536 x 1007 x 109 nanoseconds
One year = 3.1536 x 1016 ns Ans.
(c) We know that
1 year = 3.1536 x 107 seconds
1 second = 7
1years
3.1536 × 10
1 second = 3.17 x 10-8 years Ans.
Numerical Problems
Prof. Muhammad Amin 6
Chapter-1 measurement
2.1 The length and width of a rectangular plate are measured to be 15.3 cm and 12.80 cm,
respectively. Find the area of the plate.
Solution:
Length of the rectangular plate = L = 15.3 cm.
Width of the rectangular plate = w = 12.80 cm
Area of rectangular plate = A =?
We know that
A = L x W
= 15.3 x 12.80
= 195.84 cm2
A = 196 cm2 nearly Ans.
2.2 Add the following masses given in kg upto appropriate precision. 2.189, 0.089, 11.8 and 5.32
Solution:
Four masses = 2.189 kg, 0.089 kg, 5.32 kg and 11.8 kg
Sum of masses upto appropriate precision =?
Total mass = 2.189 + 0.089 + 11.8 + 5.32 = 19.398 kg
Since mass of least precision is 11.8 kg, because it has one decimal place. Therefore, the
total mass should be one decimal place, which is the appropriate precision.
Total mass = 19.4 kg Ans.
2.3 What are the dimensions and units of gravitational constant G in the formula 1 2
2
m mF = G
r
Solution:
Data: Gravitational force = 1 2
2
m mF = G
r
To Find:
Dimensions of G =?
Units of G =?
Calculation:
Dimensions of Gravitational constant(Dimensions of force)(Dimension of Length)
=(Dimensions of mass)(Dimension of mass)
2[F][L ]
[G] =[M][M]
[F] = [MLT-2]
-2 2
2
[MLT ][L ][G] =
[M ]
-1 3 -2[G] = [M L T ] Ans.
UNIT OF G: As we know that the S.I units of force, length and mass are Newton, meter and kilogram
respectively. So using the formula 2
1 2
FrG =
m m
Unit of G = Nm2/kg2 Ans
2.4 Show that the famous “Einstein equation” E = mc2 is dimensionally consistent.
Solution:
E = mc2
Dimensions of L.H.S. = E = [M L2 T-2]
∵(E = W = Fd = ma x d = [M][LT-2][L])
Dimensions of R.H.S. = mc2
=[M][LT-1]2 = [M L2 T-2]
Since the dimensions of both sides are same, therefore the equation is dimensionally consistent.