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TOPIC WISE MULTIPLE CHOICE QUESTIONS
1.6 PRECISION AND ACCURACY
(1) A precise measurement is one which has
(a) less precision (b) maximum precision
(c) less absolute uncertainty (d) both ‘a’ and ‘c’
(2) In printing we use colours which are in number
(a) 1 (b) 2
(c) 3 (d) 4
(3) The least count of meter rod is
(a) 0. 1 cm (b) 0.01 cm
(c) cannot be zero (d) can be zero
(4) The absolute uncertainty of screw gauge is
(a) 0.01 cm (b) 0.01 mm
(c) 0.001 mm (d) 0.1 cm
(5) Any measurement taken from an instrument will be more precise, if instrument has
(a) large absolute uncertainty (b) small least count
(c) both a and b (d) none of these
(6) The relation for fractional uncertainty can be given by
(a)
absolute uncertainty
measured value
(b)
measured value
absolute uncertainty
(c)
least count
absolute uncertainty
(d)
measured value
least count
1.7 ASSESSMENT OF TOTAL UNCERTAINTY IN THE FINAL RESULT
(7) There are four readings of a micrometer to measure the diameter of a wire in mm are
1.21, 1.23, 1.25, 1.23. The mean of deviations is: MTN-2019 (G-II)
(a) 0.02 mm (b) 0.01 mm
(c) 0.10 mm (d) 0.20 mm
(8) In addition and subtraction resultant uncertainty is obtained by
(a) adding absolute uncertainties (b) subtraction of absolute uncertainties
(c) addition of % age uncertainties (d) multiplication of % age uncertainties
(9) Velocity of object has 2% uncertainty and mass has 1% uncertainty. Total % age
uncertainty in K.E is
(a) 3% (b) 4%
(c) 5% (d) 6%
(10) For total assessment of uncertainty in the final result obtained by multiplication and
division (LHR 2014)
(a) add absolute uncertainty (b) add percentage unccertainty
(c) subtract absolute uncertainty (d) add fractional uncertainty
(11) Length of a side of a cube is 20mm. Its volume is
(a) 80mm
3 (b) 8cm
3
(c) 8m
3 (d) 800m
3
(12) The uncertainty in timing process can be determined by
(a) dividing the L.C of timing device by number of vibrations
(b) dividing the number of vibration by L.C of timing device
(c) multiplying the L.C of timing device with number of vibration
(d) adding the L.C of timing device by number of vibration
(13) The percentage uncertainty in measurement of mass and velocity are 2% and 3%.
The maximum uncertainty in the measurement of kinetic energy is (LHR 2013)
(a) absolute uncertainties are added (b) fractional uncertainties are added
(c) % age uncertainties are added (d) errors are added
1.8 DIMENSIONS OF PHYSICAL QUANTITIES
(14) Dimension analysis helps in
(a) deriving the formula
(b) to convert one system of unit into another
(c) to confirm the correctness of any physical equation
(d) all of these
(15) The dimension of force is (GRW 2014)
(a)
2 2 ML T
(b)
1 MLT
(c)
2 MLT
(d)
2 2 ML T
(16) Physical quanti ty “pressure” is terms of base unit is: LHR-2018 (G-I)
(a) kg
2 ms
(c) kg
2 m
(17) Dimension of frequency is same that of
(a) time period (b) angular velocity
(c) angular acceleration (d) mass
(18) Which pair has same unit: LHR-2019 (G-II)
(a) work and power (b) momentum and impulse
(c) force and torque (d) torque and power
(19) Mass is highly concentrated form of: RWP-2019 (G-I)
(a) Inertia (b) Energy
(c) Plasma (d) Charge
(20) Pressure has dimension
(a)
2 2 ML T
(b)
2 2 ML T
(c)
1 2 ML T
(d)
2 2 ML T
ANSWER KEYS
(Topic Wise Multiple Choice Questions)
1 d 16 d 31 b
2 d 17 b
3 a 18 b
4 b 19 b
5 b 20 c
6 a 21 d
7 b 22 d
8 a 23 d
9 c 24 b
10 b 25 a
11 b 26 d
12 a 27 c
13 c 28 d
14 d 29 b
15 c 30 d
SHORT QUESTIONS
(From Textbook Exercise)
1.4 Three students measured the length of a needle with scale on which minimum
division is 1mm and recorded as (i) 0.2145m (ii) 0.21 m (iii) 0.214 m. Which record is
correct and why?
Ans: In these records (iii) 0.214 m is more correct because the least count of scale is 1mm which
can be written as 0.001m. So we can measure the length upto three decimal places.
1.7 Does a dimensional analysis give any information on constant of proportionally that
may appear in algebraic expression? Explain.
Ans: Dimensional analysis does not give any information about the constant of proportionality
k. This constant k can be determined experimentally.
Example
The relation for the time period of a simple pendulum is given as
cosntant
g
l
T
The numerical value of constant in the above relation cannot be measured by dimensional
analysis, however, it can be found by experiments.
1.8 Write the dimensions of (i) Pressure (ii) Density
Ans: (i) Pressure (ii) Density
2 2
2
1 2
2
(i) As pressure
^
F P A F P A
But F MLT and A L
MLT
P ML T
L
(ii) As density is given by
m / V
m
V
3 But , m M , and V L
(^3)
3
M
ML
L
^ ^
(3) When a measurement is said to be precise? DGK-2018 (G-I)
Ans: A measurement is said to be precise when it has less precision. e.g. in order to get a
precise measurement, the more precise instrument must be used, i.e. smaller the physical
quantity, more precise instrument must be used.
(4) What is the limitation of measuring Instrument?
Ans. Every device capable to measure physical quantity like length, mass, time and
temperature has some limit of precision.
1.7 ASSESSMENT OF TOTAL UNCERTAINTY IN THE FINAL RESULT
(5) Add the masses given in kg upto appropriate precision 2.189,0.089, 11.8 and 5.
BWP-2012, GRW-
Ans: Total mass = 2.189 + 0.089 +11.8+5.32 = 19.390 kg
As least precision is 11.8 kg, having one decimal place. Therefore, the total mass must
have one decimal place which is the appropriate precision.
Total mass = 19.4 kg
(6) What will be the percentage uncertainty in a radius of a small sphere measured as
2.25cm by a Vernier caliper with least count 0.01 cm? BWP-2017 (G-I)
Ans: If the radius of a small sphere is measured as 2.25 cm by a Vernier callipers with least
count0.01 cm then
the radius r is recorded asr 2.25 0.01cm
Absolute uncertainty = Least count = 0.01 cm
%age uncertainty in
0.01cm 100
r 0.4%
2.25cm 100
(7) Given that V = (5.2 0.1) volt. Find its percentage uncertainty. BWP-2019 (G-I)
Ans: The percentage uncertainty of the voltage is measuring by this formula
Percentage uncertainty for
least count
V 100%
measuring value
V = 5.2 0.1 V
The % age uncertainty for V =
0.1V 100
×
5.2V 100
= about 2 %
(8) How can we find uncertainty in a time period?
Ans: The uncertainty in a time period is found by dividing the least count of timing device by
its number of vibrations.
i.e
Least count of timing device
Uncertainty =
Number of vibrations
1.8 DIMENSIONS OF PHYSICAL QUANTITIES
(9) Write any three uses of dimensional analysis?
Ans: The uses of dimensional analysis are
(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.
(10) Find the dimension of gravitational constant. MTN-2016 (G-II)
Ans:
1 2
2
Gm m
F =
r
2
1 2
Fr G = .......... i
m m
AsF = ma
-2 2
2
-1 3 -
F = MLT
So, from equation (i)
MLT L
G =
M
Therefore
G = M L T
(11) What is dimension of angle? Derive it.
Ans: The angular displacement ‘ ’ can be related by the linear displacement’s by the relation
S = r ………….(i)
Where ‘r’ is the radius of circle.
From equation (i), the angle made at the centre of a circle can give the valve of angular
displacement as
Length of arc AB
Radius of circle
S
r
1
(^)
L (^) S L
L r^ L
Hence is dimensionless
(12) Write any two drawbacks of dimensional analysis?
Ans: (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.
(13) What is meant by dimensions of physical quantities?
Ans: Each base quantity is considered as dimension denoted by specific symbol written with in the
square brackets. Its stands for the qualitative nature of the physical quantity.
Dimension of length is ‘L’ expressed as [L]
Dimension of mass is ‘M’ expressed as [M]
and Dimension of time is ‘T’, expressed as [T]
(14) What is meant by dimensional analysis?
Ans: Method to check the correctness of a given formula or an equation and to derive it using
the dimensions of involved physical quantities is called dimensional analysis.
B
r
θ
S
A
Hence,
Dimensions of L.H.S. = Dimensions of R.H.S
Or [LT
Thus we find that dimensions of all the three terms are the same which proves the
correctness of the equation vf = vi + at
(19) Find the dimensions of coefficient of viscosity i.e.F = 6 π ηr v
BWP-2015, SWL-2013, 2016 (G-I),MTN-
Ans: 6 π is a number having no dimensions. It is not accounted in dimensional analysis. Then
F
η =
rv
or Substituting the dimensions of F, r and v in R.H.S.
-1 -
MLT
η ML T
L LT
^
Thus, the SI unit of coefficient of viscosity is kg m
1 s
1 .
(20) Check the correctness of relation
f V
m
DGK-2016 (G-II)
Ans: Dimensions of L.H.S of the equation= [v] = [LT
1 ]
Dimensions of R.H.S of the equation =
1
(^12) ( F l [ m ])
^
1
-2 -1 2 - = MLT L M = LT
Since the dimensions of both sides of the equation are the same, hence equation is
dimensionally correct.
(21) State the principle of homogeneity of dimensions.
Ans: In order to check the correctness of an equation, we are 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.
