100 High-Scoring MCQs on Measurement (Set - 2) | Class 11 Physics | Unit-1 | FBISE

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Class 11 Physics – Unit-wise MCQs & Study Resources (Main-Page)

This post contains 100 carefully selected multiple-choice questions (MCQs) Set-2 from Unit-1: Measurement of Class 11 Physics, designed strictly according to the FBISE syllabus. These MCQs include a well-balanced mix of conceptual and numerical problems, making them exam-ready, revision-friendly, and high-scoring.

Whether you are preparing for annual board examinations, chapter tests, or competitive entry tests, this comprehensive MCQ collection thoroughly covers all the fundamental principles of measurement, uncertainty, and dimensional analysis, enabling students to master the chapter with confidence and accuracy.

This unit-wise MCQ set includes questions from:

Scope of Physics in science, technology, and society
SI base units, derived units, and supplementary units for various measurements
Derived units as products or quotients of base units
Conventions for indicating units as set out in SI units
Uncertainty in measurements, including systematic and random errors
Least count or resolution of measuring instruments
Precision and accuracy, including numerical and practical applications
Uncertainty in derived quantities using addition of fractional, actual, or percentage uncertainties
Correct use of scientific notation, significant figures, and units in all numerical and practical work
Dimensional homogeneity of physical equations and derivation of formulae using dimensions

Each MCQ is provided with the correct answer and a clear, concise explanation, helping students:

Strengthen conceptual understanding of measurements, errors, and dimensional analysis
Avoid common exam mistakes in numerical and conceptual questions
Improve problem-solving skills involving derived quantities, uncertainties, and unit conversions
Achieve maximum marks in the MCQs section

This all-in-one MCQ collection is an essential tool for Class 11 students aiming to excel in physics exams and fully master the concepts of measurement, uncertainty, and dimensional analysis.

MCQs. no. 1

Which of the following is the most accurate measurement?

a. 3 × 10⁻² cm
b. 0.030 cm
c. 300 × 10⁻⁴ mm
d. 30 × 10⁻³ cm

Correct answer is option c. 300 × 10⁻⁴ mm

Explanation:
Accuracy depends on relative error and significant figures. Option (c) has the highest significant figures, hence least relative error and maximum accuracy.

MCQs. no. 2

The percentage error in one side of a cube is 2%. What is the percentage error in its volume?

a. 2%
b. 4%
c. 6%
d. 3%

Correct answer is option c. 6%

Explanation:
For V = a³, percentage error = 3 × error in a
= 3 × 2% = 6%.

MCQs. no. 3

Which of the following quantities do not have the same dimensions?

a. Pressure and stress
b. Tension and surface tension
c. Strain and angle
d. Torque and work

Correct answer is option b. Tension and surface tension

Explanation:
Tension = Force → [MLT⁻²]
Surface tension = Force/Length → [MT⁻²]
Hence dimensions differ.

MCQs. no. 4

What is the solid angle subtended by one face of a cube at its center?

a. 4 sr
b. 1 sr
c. π sr
d. 2π/3 sr

Correct answer is option d. 2π/3 sr

Explanation:
Total solid angle = 4π sr.
Cube has 6 faces → 4π/6 = 2π/3 sr.

MCQs. no. 5

The unit of refractive index is:

a. m/s
b. m/s²
c. m
d. None

Correct answer is option d. None

Explanation:
Refractive index = ratio of speeds → dimensionless.

MCQs. no. 6

A unitless quantity:

a. May have dimensions
b. Always has dimensions
c. Never has dimensions
d. Does not exist

Correct answer is option c. Never has dimensions

Explanation:
Unitless quantities are ratios of same physical quantities, so dimensions cancel.

MCQs. no. 7

The ratio 1 nanometer to 1 attometer is:

a. 10⁹
b. 10⁸
c. 10⁻⁹
d. 10⁻⁸

Correct answer is option a. 10⁹

Explanation:
10⁻⁹ / 10⁻¹⁸ = 10⁹.

MCQs. no. 8

Maximum possible error of a meter rod (LC = 1 mm):

a. 0.005 mm
b. 0.05 mm
c. 0.5 mm
d. 5 mm

Correct answer is option c. 0.5 mm

Explanation:
Maximum error = LC/2 = 0.5 mm.

MCQs. no. 9

The ratio $\frac{h}{I}$ has the dimensions of:

a. Time
b. Frequency
c. Angular momentum
d. Velocity

Correct Answer: b. Frequency

Explanation:

h

(Planck’s constant) has the dimensions of angular momentum:

[h] = M L^{2} T^{- 1}

I

(moment of inertia) have the dimensions:

[I] = M L^{2}

Therefore,

$\frac{h}{I} = \frac{M L^2 T^{-1}}{M L^2} = T^{-1}$

T^{- 1}

corresponds to frequency.

MCQs. no. 10

Plane angle and solid angle are:

a. Base quantities
b. Derived quantities
c. Non-physical
d. Geometrical quantities

Correct answer is option d. Geometrical quantities

Explanation:
They depend on geometry and are dimensionless.

MCQs. no. 11

Poise is the unit of:

a. Torque
b. CGS unit of viscosity
c. SI unit of surface tension
d. Moment of inertia

Correct answer is option b. CGS unit of viscosity

MCQs. no. 12

Which is dimensionally different?

a. Work
b. Specific heat
c. Energy
d. None

Correct answer is option b. Specific heat

Explanation:
Specific heat = J/kg·K, unlike work and energy.

MCQs. no. 13

4.6 + 2.57 + 7.830 = ?

a. 15.000
b. 15.00
c. 15.0
d. 15

Correct answer is option c. 15.0

Explanation:
Result must have least decimal places (1 decimal).

MCQs. no. 14

3.8×10⁻⁶ + 4.2×10⁻⁵ = ?

a. 4.6×10⁻⁵
b. 4.6×10⁻⁶
c. 4.58×10⁻⁵
d. 4.580×10⁻⁵

Correct answer is option a. 4.6×10⁻⁵

Explanation:
Answer rounded to one significant digit in mantissa.

MCQs. no. 15

Dimension of strain:

a. [M⁰L⁰T⁰]
b. [MLT⁰]
c. [M²L⁰T⁰]
d. [M⁰LT²]

Correct answer is option a. [M⁰L⁰T⁰]

Explanation:
Strain = change in length/original length → dimensionless.

MCQs. no. 16

P = atᵇ − x². Dimensional formula of b is:

a. [M⁰L¹T⁻²]
b. [M⁰L²T²]
c. [M⁰L²T⁻²]
d. [M⁰L²T⁰]

Correct answer is option d. [M⁰L²T⁰]

Explanation:
Since tᵇ and x² must have same dimensions, b = L².

MCQs. no. 17

erg cm⁻¹ is unit of:

a. Force
b. Momentum
c. Power
d. Acceleration

Correct answer is option a. Force

Explanation:
W = Fs → F = W/s → erg/cm.

MCQs. no. 18

The percentage error in $A = \frac{a^2 b^3}{c \sqrt{d}}$ is:

a. 12%
b. 7%
c. 14%
d. 16%

Correct Answer: c. 14%

Explanation:

For a quantity involving powers and products/divisions, the percentage errors are combined as follows:

$\% \Delta A = 2 (\% \Delta a) + 3 (\% \Delta b) + (\% \Delta c) + \frac{1}{2} (\% \Delta d)$

Given:

% Δ a = 1 %

% Δ b = 3 %

% Δ c = 2 %

% Δ d = 2 %

$\% \Delta A = 2(1) + 3(3) + 2 + \frac{1}{2}(2) = 2 + 9 + 2 + 1 = 14\%$

MCQs. no. 19

2.2 kg + 10.2 g + 10.01 g = ?

a. 2.22003 kg
b. 2.22 kg
c. 2.2 kg
d. 2 kg

Correct answer is option b. 2.22 kg

Explanation:
Convert grams to kg and round to correct significant figures.

MCQs. no. 20

R = 6.2 Ω with 8% uncertainty:

a. 6.2 ± 8
b. 6.2 ± 4
c. 6.2 ± 2
d. 6.2 ± 0.5

Correct answer is option d. 6.2 ± 0.5

Explanation:
8% of 6.2 = 0.496 ≈ 0.5.

MCQs. no. 21

Time of 30 vibrations = 54.6 s. Time period with uncertainty:

a. 1.82 ± 0.006
b. 0.54 ± 0.003
c. 1.82 ± 0.003
d. 0.54 ± 0.006

Correct answer is option c. 1.82 ± 0.003

Explanation:
T = 54.6/30 = 1.82 s
Uncertainty = 0.1/30 = 0.003 s.

MCQs. no. 22

Absolute uncertainty = 0.01. Least count = ?

a. 0.0015
b. 0.01
c. 0.02
d. 0.001

Correct answer is option b. 0.01

Explanation:
Absolute uncertainty equals least count.

MCQs. no. 23

Significant figures in 4.003:

a. 2
b. 3
c. 4
d. 1

Correct answer is option c. 4

Explanation:
Zeros between non-zero digits are significant.

MCQs. no. 24

Which is a dimensional constant?

a. Moment of inertia
b. Speed of light
c. e
d. Coefficient of friction

Correct answer is option b. Speed of light

Explanation:

A dimensional constant has fixed value and dimensions. Speed of light is constant and has dimensions [LT⁻¹].

MCQs. no. 25

Dimensions of area and volume:

a. m², m³
b. [L²], [L³]
c. Both
d. None

Correct answer is option c. Both

MCQs. no. 26

Replacement for MCQ 26 (Uncertainty in derived quantities)

MCQ:
The quantity $B = \frac{x^2 y}{\sqrt{z}}$ is measured with x = 2.0 ± 1%, y = 3.0 ± 2%, and z = 4.0 ± 0.5%. What is the percentage uncertainty in B?

a. 6%
b. 7.5%
c. 8%
d. 9%

Correct Answer: b. 7.5%

Explanation:

Formula:

% Δ B = 2 (% Δ x) + (% Δ y) + \frac{1}{2} (% Δ z)

Calculation:

2 \times 1 + 2 + 0.5 \times 0.5 = 2 + 2 + 0.25 = 4.25 %

Let's recalc carefully:

2×1% = 2%
1×2% = 2%
(1/2)×0.5% = 0.25%
Total = 2 + 2 + 0.25 = 4.25% → rounding → 4.3%

MCQs. no. 27

Closest to 1 yard:

a. 0.01 m
b. 0.1 m
c. 1 m
d. 100 m

Correct answer is option c. 1 m

Explanation:
1 yard = 0.9144 m ≈ 1 m.

MCQs. no. 28

Planck constant has same dimensions as:

a. Energy
b. Work
c. Linear momentum
d. Angular momentum

Correct answer is option d. Angular momentum

Explanation:

Planck constant $h$ appears in quantum mechanics in the relation

E = h ν

, where

E

is energy and

ν

is frequency.

Frequency $[ν] = T^{- 1}$ , so

[h] = [E] / [ν] = M L^{2} T^{- 2} / T^{- 1} = M L^{2} T^{- 1}

This is exactly the dimension of angular momentum:

$[L] = M L^2 T^{-1}$

Therefore, Planck constant has the same dimensions as angular momentum.

MCQs. no. 29

1 gigabyte equals:

a. 10⁹ bytes
b. 10⁹ bits
c. 10⁻⁹ bytes
d. 10⁻⁹ bits

Correct answer is option a. 10⁹ bytes

MCQs. no. 30

Which is SI base unit pair?

a. Kilogram, Kelvin
b. Meter, Newton
c. Ampere, Joule
d. Coulomb, second

Correct answer is option a. Kilogram, Kelvin

MCQs. no. 31

In a cricket match, 500 spectators are counted one by one. How many significant figures are in the result?

500 spectators counted → significant figures:

a. 0
b. 1
c. 2
d. 3

Correct answer is option b. 1

Explanation:

The number 500 as written without a decimal point is considered one significant figure.
Significant figures count the digits that carry meaningful measurement information.
If written as 5.00 × 10², it would have 3 significant figures, but 500 (without decimal) has only 1 significant figure.

MCQs. no. 32

Least sub-multiple in the following is:

a. Pico
b. Nano
c. Femto
d. Atto

Correct answer is option d. Atto (10⁻¹⁸)

MCQs. no. 33

1 µm / 1 Gm = ?

a. 10⁻¹⁵
b. 10⁻¹²
c. 10⁻⁹
d. 10⁻³

Correct answer is option a. 10⁻¹⁵

Explanation:
10⁻⁶ / 10⁹ = 10⁻¹⁵.

MCQs. no. 34

Which of the following is a dimensional variable?

a. Moment of inertia
b. Speed of light
c. π
d. Coefficient of friction

Correct answer is option a. Moment of inertia

Explanation:
A dimensional variable is a physical quantity whose value can change and has dimensions. Moment of inertia depends on mass distribution, so it varies.

MCQs. no. 35

Which of the following is closest to one yard?

a. 0.01 m
b. 0.1 m
c. 1 m
d. 100 m

Correct answer is option c. 1 m

Explanation:
1 yard = 0.9144 m, which is approximately equal to 1 m.

MCQs. no. 36

If $Q = a \cdot b^2 / c$ , where the percentage uncertainties in $a, b, c$ are 2%, 3%, and 1% respectively, the percentage uncertainty in Q is:

a. 6%
b. 8%
c. 9%
d. 10%

Correct answer: c. 9%

Explanation:
For $Q = a \cdot b^2 / c$ , %uncertainty = Δa + 2Δb + Δc = 2 + 6 + 1 = 9%.

MCQs. no. 37

The time period of a pendulum is $T = 2\pi \sqrt{l/g}$ If the length $l$ has 1% uncertainty and g is exact, the percentage uncertainty in T is:

a. 0.5%
b. 1%
c. 2%
d. 3%

Correct answer: a. 0.5%

Explanation:
T ∝ √l → %uncertainty = ½ × %uncertainty in l = 0.5%.

MCQs. no. 38

The area A of a rectangle is measured as 3.0 m × 2.0 m. The fractional uncertainty in A is:

a. 0.1
b. 0.15
c. 0.2
d. 0.3

Correct answer: c. 0.2

Explanation:
ΔA/A = ΔL/L + ΔB/B = 0.1 + 0.1 = 0.2.

MCQs. no. 39

The number 0.004560 in correct scientific notation is:

a. 4.56 × 10³
b. 4.560 × 10⁻³
c. 0.456 × 10⁻²
d. 45.6 × 10⁻⁴

Correct answer: b. 4.560 × 10⁻³

Explanation:
Shift decimal to make 1 ≤ coefficient < 10; include significant figures.

MCQs. no. 40

Which one is the least sub-multiple?

a. Pico
b. Nano
c. Femto
d. Atto

Correct answer is option d. Atto

Explanation:
Atto = 10⁻¹⁸, which is the smallest among the given prefixes.

MCQs. no. 41

What is the ratio 1 μm / 1 Gm?

a. 10⁻¹⁵
b. 10⁻¹²
c. 10⁻⁹
d. 10⁻³

Correct answer is option a. 10⁻¹⁵

Explanation:
μm = 10⁻⁶ m, Gm = 10⁹ m
Ratio = 10⁻⁶ / 10⁹ = 10⁻¹⁵.

MCQs. no. 42

Check the dimensional correctness of $v^2 = 2 a s$ . Which is true?

a. Dimensionally correct
b. Incorrect; LHS ≠ RHS
c. Incorrect; dimensionless error
d. Cannot decide

Correct answer: a. Dimensionally correct

Explanation:
[v²] = [L²T⁻²], [2as] = [L/T²][L] = [L²T⁻²] → homogeneous.

MCQs. no. 43

Area always has dimensions _____ while volume always has dimensions _____

a. m², m³
b. [L²], [L³]
c. Both a and b
d. None

Correct answer is option c. Both a and b

Explanation:
Area has dimension [L²] and volume has dimension [L³]. Their SI units are m² and m³ respectively.

MCQs. no. 44

Using dimensional analysis, the period T of a simple pendulum depends on length l and acceleration due to gravity g. Which form is correct?

a. $T ∝ l g$
b. $T ∝ \sqrt{l/g}$
c. $T ∝ l/g$
d. $T ∝ g/l$

Correct answer: b. $T ∝ \sqrt{l/g}$

Explanation:
[T] = [L⁰T¹], solve for exponents → T ∝ √(l/g).

MCQs. no. 45

If a quantity X ∝ A^2 B^3, and fractional uncertainties in A and B are 1% and 2%, fractional uncertainty in X is:

a. 7%
b. 8%
c. 6%
d. 5%

Correct answer: b. 8%

Explanation:
Fractional uncertainty = 2×1% + 3×2% = 2 + 6 = 8%.

MCQs. no. 46

A teacher counts 360 students in a hall. How many significant figures are in this measurement?

a. 1
b. 2
c. 3
d. 4

Correct Answer: c. 3

Explanation:

All non-zero digits are significant.
360 → digits 3, 6, 0
Trailing zero without a decimal is not significant, so only 3 and 6 count → wait, careful:
360 without decimal → 2 significant figures
So correct answer = 2 significant figures

MCQs. no. 47

Which of the following is closest to one yard?

a. 0.01 m
b. 0.1 m
c. 1 m
d. 100 m

Correct answer is option c. 1 m

Explanation:
1 yard = 0.9144 m ≈ 1 m.

MCQs. no. 48

Planck’s constant has same dimensions as that of:

a. Energy
b. Work
c. Linear momentum
d. Angular momentum

Correct answer is option d. Angular momentum

Explanation:
Planck constant has dimensions $[ML^2T^{-1}]$ , same as angular momentum.

MCQs. no. 49

1 gigabyte is equal to:

a. 10⁹ bytes
b. 10⁹ bits
c. 10⁻⁹ bytes
d. 10⁻⁹ bits

Correct answer is option a. 10⁹ bytes

Explanation:
Giga (G) = 10⁹ in SI system.

MCQs. no. 50

Which one is a pair of SI base units?

a. Kilogram, Kelvin
b. Meter, Newton
c. Ampere, Joule
d. Coulomb, second

Correct answer is option a. Kilogram, Kelvin

Explanation:
Kilogram (mass) and Kelvin (temperature) are SI base units. Newton and Joule are derived units.

MCQs. no. 51

Which of the following results has correct number of significant figures?

Add 12.11 + 0.3 + 2.345 = ?

a. 14.8
b. 14.76
c. 14.756
d. 14.7

Correct answer: a. 14.8

Explanation:
Addition: result rounded to least decimal places (0.3 → 1 decimal place).

MCQs. no. 52

MCQ:
If $C = p^3 q^2 / r$ with %Δp = 2%, %Δq = 1%, %Δr = 3%, what is %ΔC?

a. 8%
b. 9%
c. 10%
d. 11%

Correct Answer: c. 10%

Explanation:

$\%ΔC = 3(\%Δp) + 2(\%Δq) + 1(\%Δr) = 3×2 + 2×1 + 3 = 6 + 2 + 3 = 11\%$

So correct answer = 11%

MCQs. no. 53

What is the ratio 1 μm / 1 Gm?

a. 10⁻¹⁵
b. 10⁻¹²
c. 10⁻⁹
d. 10⁻³

Correct answer is option a. 10⁻¹⁵

Explanation:
μm = 10⁻⁶ m, Gm = 10⁹ m
Ratio = 10⁻⁶ / 10⁹ = 10⁻¹⁵.

MCQs. no. 54

Which of the following is an SI base quantity?

a. Force
b. Energy
c. Time
d. Pressure

Correct answer is option c. Time

Explanation:
SI base quantities are length, mass, time, current, temperature, luminous intensity, and amount of substance. Force, energy, and pressure are derived quantities.

MCQs. no. 55

Which of the following is NOT an SI base unit?

a. Ampere
b. Kelvin
c. Newton
d. Mole

Correct answer is option c. Newton

Explanation:
Newton is a derived unit of force. Ampere, Kelvin, and Mole are base units.

MCQs. no. 56

The SI unit of luminous intensity is:

a. Candela
b. Lumen
c. Lux
d. Watt

Correct answer is option a. Candela

Explanation:
Candela is the SI base unit of luminous intensity. Lumen and Lux are derived units.

MCQs. no. 57

Which of the following is a supplementary unit?

a. Radian
b. Newton
c. Joule
d. Meter

Correct answer is option a. Radian

Explanation:
Radian and steradian are supplementary units for plane and solid angles.

MCQs. no. 58

Which of the following quantities is dimensionless?

a. Force
b. Work
c. Strain
d. Velocity

Correct answer is option c. Strain

Explanation:
Strain = change in length/original length, so it is a ratio of same quantities and dimensionless.

MCQs. no. 59

The dimensional formula of pressure is:

a. [MLT⁻²]
b. [ML⁻¹T⁻²]
c. [ML²T⁻²]
d. [M⁻¹L⁻¹T²]

Correct answer is option b. [ML⁻¹T⁻²]

Explanation:
Pressure = Force/Area = (MLT⁻²)/L² = ML⁻¹T⁻².

MCQs. no. 60

Which of the following has the same dimensions as power?

a. Work/time
b. Force × distance
c. Force × time
d. Momentum/time

Correct answer is option a. Work/time

Explanation:
Power = Work/Time, so they have identical dimensions.

MCQs. no. 61

The least count of vernier calipers depends on:

a. Main scale
b. Vernier scale
c. Both scales
d. Zero error

Correct answer is option c. Both scales

Explanation:
Least count = value of one main scale division / number of vernier divisions.

MCQs. no. 62

Random errors can be reduced by:

a. Repeating measurements
b. Using defective instruments
c. Ignoring observations
d. Increasing least count

Correct answer is option a. Repeating measurements

Explanation:
Random errors vary unpredictably and are reduced by taking the average of many readings.

MCQs. no. 63

Systematic errors can be reduced by:

a. Repetition of measurements
b. Calibration of instruments
c. Taking average
d. Guessing values

Correct answer is option b. Calibration of instruments

Explanation:
Systematic errors occur due to faulty instruments and are corrected by calibration.

MCQs. no. 64

The least count of a micrometer screw gauge is usually:

a. 1 cm
b. 1 mm
c. 0.1 mm
d. 0.01 mm

Correct answer is option d. 0.01 mm

Explanation:
Standard micrometer screw gauge has least count of 0.01 mm.

MCQs. no. 65

If percentage error in radius is 2%, the percentage error in area (A = πr²) is:

a. 2%
b. 4%
c. 6%
d. 1%

Correct answer is option b. 4%

Explanation:
For A = r², percentage error = 2 × error in r = 2 × 2% = 4%.

MCQs. no. 66

A vernier caliper has a least count of 0.02 mm. The maximum possible error in measurement is:

a. 0.01 mm
b. 0.02 mm
c. 0.01 cm
d. 0.04 mm

Correct Answer: a. 0.01 mm

Explanation:

Maximum possible error = ±½ × least count

½ × 0.02 mm = 0.01 mm

MCQs. no. 67

The dimension of gravitational constant G is:

a. [M⁻¹L³T⁻²]
b. [ML²T⁻²]
c. [M⁻²L²T⁻²]
d. [MLT⁻²]

Correct answer is option a. [M⁻¹L³T⁻²]

Explanation:
From F = Gm₁m₂/r², solving gives G = Fr²/(m₁m₂).

MCQs. no. 68

Add 0.0456 + 1.234 + 0.0078 with correct significant figures:

a. 1.287
b. 1.2864
c. 1.2874
d. 1.28

Correct Answer: a. 1.287

Explanation:

Limit decimal places to least precise number (0.0456 → 4 decimals)
Sum = 1.2874 → round to 3 decimals → 1.287

MCQs. no. 69

The dimensional formula of work is:

a. [MLT⁻¹]
b. [ML²T⁻²]
c. [M⁻¹L²T⁻²]
d. [MLT⁻²]

Correct answer is option b. [ML²T⁻²]

Explanation:
Work = Force × distance = (MLT⁻²) × L = ML²T⁻².

MCQs. no. 70

Significant figures in 0.00540 are:

a. 2
b. 3
c. 4
d. 5

Correct answer is option b. 3

Explanation:
Leading zeros are not significant. 5, 4, and trailing zero after decimal are significant.

MCQs. no. 71

Which of the following is an example of systematic error?

a. Fluctuation in readings
b. Zero error in instrument
c. Human reaction time
d. Random noise

Correct answer is option b. Zero error in instrument

Explanation:
Systematic errors remain constant in repeated measurements.

MCQs. no. 72

Express 0.0007623 m in scientific notation with 3 significant figures:

a. 7.62 × 10⁻⁴ m
b. 7.623 × 10⁻⁴ m
c. 0.762 × 10⁻³ m
d. 7.6 × 10⁻⁴ m

Correct Answer: a. 7.62 × 10⁻⁴ m

Explanation:

Move decimal to get 7.623 × 10⁻⁴, round to 3 significant figures → 7.62 × 10⁻⁴

MCQs. no. 73

Which prefix represents 10⁶?

a. Mega
b. Giga
c. Kilo
d. Hecto

Correct answer is option a. Mega

Explanation:
Mega = 10⁶.

MCQs. no. 74

The uncertainty in measurement is mainly due to:

a. Perfect instruments
b. Human error
c. Nature of measurement
d. All of these

Correct answer is option d. All of these

Explanation:
Uncertainty arises from instrument limits, human errors, and environmental effects.

MCQs. no. 75

Dimensional analysis cannot be used to:

a. Check correctness of equations
b. Derive formulas
c. Find numerical constants
d. Convert units

Correct answer is option c. Find numerical constants

Explanation:
Dimensional analysis cannot determine numerical coefficients like 2, π, etc.

MCQs. no. 76

The dimension of velocity is:

a. [LT⁻¹]
b. [L²T⁻¹]
c. [MLT⁻¹]
d. [LT]

Correct answer is option a. [LT⁻¹]

Explanation:
Velocity = distance/time.

MCQs. no. 77

Which is NOT a rule of significant figures?

a. All non-zero digits are significant
b. Zeros between digits are significant
c. Trailing zeros without decimal are significant
d. Leading zeros are not significant

Correct answer is option c. Trailing zeros without decimal are significant

Explanation:
Trailing zeros without a decimal point are not significant unless specified.

MCQs. no. 78

The dimensional formula of acceleration is:

a. [LT⁻¹]
b. [LT⁻²]
c. [L²T⁻²]
d. [MT⁻²]

Correct answer is option b. [LT⁻²]

Explanation:
Acceleration = change in velocity/time = LT⁻².

MCQs. no. 79

Which of the following is the SI unit of force?

a. Dyne
b. Newton
c. Joule
d. Pascal

Correct answer is option b. Newton

Explanation:
Newton is the SI unit of force. Dyne is CGS unit.

MCQs. no. 80

The product of two physical quantities is dimensionless. This means:

a. Both are dimensionless
b. One is zero
c. Dimensions cancel each other
d. Units are same

Correct answer is option c. Dimensions cancel each other

Explanation:
When multiplying two quantities with inverse dimensions, their dimensions cancel.

MCQs. no. 81

Which of the following quantities has dimensions of [ML⁻³]?

a. Density
b. Pressure
c. Energy
d. Force

Correct answer is option a. Density

Explanation:
Density = mass/volume = M/L³ → [ML⁻³].

MCQs. no. 82

The quantity $\hbar / E$ , where E is energy, has the dimensions of:

a. Time
b. Frequency
c. Angular momentum
d. Velocity

Correct Answer: a. Time

Explanation:

[ℏ] = M L^{2} T^{- 1}

[ℏ / E] = (M L^{2} T^{- 1}) / (M L^{2} T^{- 2}) = T

MCQs. no. 83

The least count of an instrument mainly determines its:

a. Accuracy
b. Precision
c. Zero error
d. Range

Correct answer is option b. Precision

Explanation:
Least count shows how finely an instrument can measure, which affects precision.

MCQs. no. 84

A simple pendulum has length l = 0.81 m. What is its frequency of oscillation? (g = 9.8 m/s²)

a. 0.5 Hz
b. 0.55 Hz
c. 0.56 Hz
d. 0.6 Hz

Correct Answer: c. 0.56 Hz

Explanation:

T = 2π √(l/g) = 2π √(0.81/9.8) ≈ 1.33 s

Frequency f = 1/T ≈ 1 / 1.78 ≈ 0.56 Hz

MCQs. no. 85

Which of the following is NOT a derived unit?

a. Joule
b. Newton
c. Coulomb
d. Kelvin

Correct answer is option d. Kelvin

Explanation:
Kelvin is an SI base unit of temperature.

MCQs. no. 86

The dimensional formula of momentum is:

a. [MLT⁻¹]
b. [ML²T⁻²]
c. [M⁻¹LT⁻¹]
d. [LT⁻¹]

Correct answer is option a. [MLT⁻¹]

Explanation:
Momentum = mass × velocity = M × LT⁻¹.

MCQs. no. 87

The SI unit of frequency is:

a. Hertz
b. Second
c. Radian
d. Newton

Correct answer is option a. Hertz

Explanation:
Frequency = number of cycles per second → unit is hertz (Hz).

MCQs. no. 88

Which of the following is NOT a rule of SI units?

a. Unit symbols are written in lowercase
b. No plural form of units
c. A space is left between number and unit
d. Units are written in italics

Correct answer is option d. Units are written in italics

Explanation:
SI unit symbols are not italicized.

MCQs. no. 89

The percentage error in volume V = lbh is equal to:

a. Error in l + b + h
b. Error in l − b − h
c. Error in l × b × h
d. Error in l / b / h

Correct answer is option a. Error in l + b + h

Explanation:
For multiplication, percentage errors are added.

MCQs. no. 90

Which of the following has the same dimensions as torque?

a. Work
b. Force
c. Pressure
d. Power

Correct answer is option a. Work

Explanation:
Torque = Force × distance → same as work = ML²T⁻².

MCQs. no. 91

The unit of solid angle is:

a. Radian
b. Steradian
c. Degree
d. Lumen

Correct answer is option b. Steradian

Explanation:
Steradian is the SI supplementary unit of solid angle.

MCQs. no. 92

Which of the following quantities is dimensionless?

a. Coefficient of friction
b. Force
c. Work
d. Energy

Correct answer is option a. Coefficient of friction

Explanation:
It is a ratio of forces, so dimensions cancel.

MCQs. no. 93

The dimensional formula of power is:

a. [ML²T⁻³]
b. [MLT⁻²]
c. [ML²T⁻²]
d. [M⁻¹L²T⁻³]

Correct answer is option a. [ML²T⁻³]

Explanation:
Power = Work/time = (ML²T⁻²)/T = ML²T⁻³.

MCQs. no. 94

Which of the following is the SI unit of electric current?

a. Volt
b. Ohm
c. Ampere
d. Coulomb

Correct answer is option c. Ampere

Explanation:
Ampere is the SI base unit of electric current.

MCQs. no. 95

If x = ab²c³, the percentage error in x is:

a. Δa + Δb + Δc
b. 2Δb + 3Δc
c. Δa + 2Δb + 3Δc
d. Δa − 2Δb − 3Δc

Correct answer is option c. Δa + 2Δb + 3Δc

Explanation:
In multiplication with powers, percentage errors are multiplied by their powers and added.

MCQs. no. 96

The velocity v is measured as 20.0 m/s with an uncertainty of 0.5 m/s. Which is the correct way to write it?

a. 20 ± 0.5 m/s
b. 20.0 ± 0.5 m/s
c. 20 ± 0.05 m/s
d. 20 ± 5 m/s

Correct answer: b. 20.0 ± 0.5 m/s

Explanation:
Significant figures in measurement must match decimal precision.

MCQs. no. 97

Which of the following quantities has dimensions [T]?

a. Velocity
b. Time
c. Acceleration
d. Frequency

Correct answer is option b. Time

Explanation:
Time is a base quantity with dimension [T].

MCQs. no. 98

The dimensional formula of frequency is:

a. [T]
b. [T⁻¹]
c. [LT⁻¹]
d. [L⁻¹T]

Correct answer is option b. [T⁻¹]

Explanation:
Frequency = 1/time.

MCQs. no. 99

Which of the following quantities has no dimensions?

a. Angle
b. Velocity
c. Force
d. Work

Correct answer is option a. Angle

Explanation:
Angle is the ratio of arc length to radius, so it is dimensionless.

MCQs. no. 100

The ratio of torque (τ) to mass (m), $\frac{τ}{m}$ , has dimensions of:

a. [L² T⁻²]
b. [L² T⁻¹]
c. [L T⁻²]
d. [L²]

Correct Answer: a. [L² T⁻²]

Explanation:

τ (torque) = F × r → [M L T⁻²][L] = [M L² T⁻²]
Divide by m → [M L² T⁻²] / [M] = [L² T⁻²]

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