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Units and Measurement: questions with answers

Class 11 Physics, Chapter 1 (NCERT). 15 questions by concept, 2 with pictures. Open “Show answer” for the answer and why.

How to teach this chapter · Common misconceptions & worked visual for this chapter

Measurement standards and SI units

Question 1

Which pair gives the SI base units for mass and electric current, in that order?

  1. (a)kg, mA
  2. (b)kg, A
  3. (c)g, A
Show answer

(b) kg, A

The SI base unit of mass is kilogram (kg). The SI base unit of electric current is A.

Question 2

A mass is recorded as 20 g. Which report expresses the same mass using the SI base unit?

  1. (a)20 kg
  2. (b)20 g
  3. (c)0.020 kg
Show answer

(c) 0.020 kg

Use kilogram for the SI base unit of mass. Divide the gram value by 1000 to obtain 0.020 kg.

Indirect measurement, magnification and instrument precision

Question 3

A small image has area 9 cm² and its enlarged projection has area 900 cm². What is the linear magnification?

  1. (a)100
  2. (b)10
  3. (c)1/100
Show answer

(b) 10

The area ratio is the square of the linear magnification. Take the positive square root of 900 / 9; both areas already use cm².

Question 4

A projector produces a linear magnification of 10. What is projected area/original area?

  1. (a)1/100
  2. (b)100
  3. (c)10
Show answer

(b) 100

Each of the two linear dimensions is multiplied by 10. The area ratio is therefore 10².

Rounding and preserving guard digits

Question 5

A measured value 9.58 will be inverted and then used in another calculation whose final result needs 3 significant figures. Which intermediate-rounding procedure is appropriate?

  1. (a)Round every intermediate to the final significant-figure count; this cannot affect the answer.
  2. (b)Round intermediates to one significant figure to remove uncertain digits early.
  3. (c)Retain at least one extra significant digit, then round the final result.
Show answer

(c) Retain at least one extra significant digit, then round the final result.

Intermediate truncation or rounding can affect later arithmetic. Keep a guard digit beyond the final precision and round only the completed result.

Question 6

A learner calculates 1/7.13 as 0.140, then takes its reciprocal and obtains 7.14 instead of 7.13. What best explains the mismatch?

  1. (a)Taking a reciprocal changes the original physical quantity irreversibly even with exact arithmetic.
  2. (b)Intermediate rounding cannot change a later result, so this must be new measurement error.
  3. (c)Rounding the intermediate reciprocal lost information needed by the next step.
Show answer

(c) Rounding the intermediate reciprocal lost information needed by the next step.

Taking two exact reciprocals returns the original nonzero number. The mismatch is introduced by rounding the intermediate value too early.

Significant figures and scientific notation

Question 7

How many significant figures are in the reported measurement 0.007 m²?

  1. (a)4
  2. (b)2
  3. (c)1
Show answer

(c) 1

Leading zeros only locate the decimal point. Count the digits from the first nonzero digit, including zeros between nonzero digits.

Question 8

Which scientific-notation report preserves both the magnitude and the stated precision of 0.007 m²?

  1. (a)7.000 × 10⁻³ m²
  2. (b)7 × 10⁻³ m²
  3. (c)7 × 10³ m²
Show answer

(b) 7 × 10⁻³ m²

Moving the decimal point changes the power of ten, not the measured precision. Do not turn leading place-holding zeros into additional significant trailing zeros.

Significant-figure arithmetic and relative uncertainty

Question 9

Two measurements are A = 20 ± 2 units and B = 100 ± 2 units. How do their percentage uncertainties compare?

  1. (a)Their percentage uncertainties are equal because the absolute uncertainties match.
  2. (b)A has the larger percentage uncertainty.
  3. (c)B has the larger percentage uncertainty.
Show answer

(b) A has the larger percentage uncertainty.

Percentage uncertainty is absolute uncertainty divided by measured magnitude, multiplied by 100. For the same absolute uncertainty, the smaller measurement A has the larger percentage uncertainty.

Dimensional formulae from physical definitions

Question 10

In x = ct², x is length and t is time. What are the dimensions of the coefficient c?

  1. (a)[L]
  2. (b)[L T^-2]
  3. (c)[L T^2]
Show answer

(b) [L T^-2]

The coefficient multiplies the stated variable or variable power. Divide the dimensions of the complete term by those of that factor, giving [L T^-2].

Dimensionless angles and angular change

Question 11

Two stationary objects lie nearly along the same viewing direction. Object B is 2 times as far away as A. For the same small transverse observer displacement, what is the ratio angular shift(A) : angular shift(B)?

Same observer movement, two objectsObserver positions O and O′ are separated by b in both panels. A is at distance d, and B is at 2d. QUESTION DIAGRAM Same observer movement, two objects Ray geometry schematic · not to scale Object A O O′ b A d Object B O O′ b B 2d
  1. (a)1 : 2
  2. (b)1 : 1
  3. (c)2 : 1
Show answer

(c) 2 : 1

For the same small transverse observer displacement b, angular shift is approximately b/d.

Here d_B = 2d_A, so θ_A/θ_B = d_B/d_A = 2.

The angular-shift ratio A:B is therefore 2:1; the nearer object has the larger parallax.

Therefore, the requested answer is 2 : 1.

Question 12

For the same small transverse observer displacement, stationary object A shows 2 times the angular shift of B. What is the ratio distance(A) : distance(B)?

Compare the direction changesAt a common drawing origin, A changes direction by 2α and B by α for the same observer displacement. QUESTION DIAGRAM Compare the direction changes Directions compared at a common origin Object A 2α Earlier direction Object B α Earlier direction
  1. (a)1 : 2
  2. (b)2 : 1
  3. (c)1 : 1
Show answer

(a) 1 : 2

For equal small transverse observer displacement, angular shift is inversely proportional to distance: θ ≈ b/d.

The supplied angular-shift ratio is θ_A:θ_B = 2:1.

Reverse that ratio for distance: d_A:d_B = 1:2.

Therefore, the requested answer is 1 : 2.

Dimensional homogeneity and limits of checking

Question 13

A model contains log of an argument built from two quantities: v and c are speeds. Which argument is dimensionally admissible?

  1. (a)v/c
  2. (b)v × c
  3. (c)v
Show answer

(a) v/c

A trigonometric, exponential or logarithmic argument must be dimensionless. Divide quantities of the same dimensions to form the required ratio.

Converting powered and compound units

Question 14

A new system uses mass unit 2 kg, length unit 1 m and time unit 1 s. What is the numerical measure of an energy of 84 J in the new energy unit?

  1. (a)42
  2. (b)84
  3. (c)168
Show answer

(a) 42

Energy has dimensions ML²T⁻². One new energy unit is 2 × 1² / 1² joules; divide the energy by this unit size.

Deriving power laws and estimating physical scales

Question 15

Assume a pendulum period depends only on length l, gravitational acceleration g and bob mass m as a product of powers. At fixed l and g, bob mass is multiplied by 4. What is new period/old period?

  1. (a)1/4
  2. (b)1
  3. (c)4
Show answer

(b) 1

Time has no mass dimension, and m is the only mass-bearing input. Its exponent must be zero, so the period does not change.

Common misconception in Units and Measurement

Open full misconception guide →

Do more decimal places guarantee accuracy?

Wrong

A reading of 10.50 cm must be accurate because it includes hundredths.

Why it feels right. I associate fine resolution with closeness to the true value.

Right

A precise measurement can still have a systematic error.

Worked example

The three readings form a tight cluster around the wrong value.
  1. An instrument reads 10.49, 10.50 and 10.51 cm on a 10.00 cm standard.
  2. The readings cluster tightly, but the average is 0.50 cm too high.