Chapter 1: Units and Measurement Assertion-Reason Questions | physics Class 11 CBSE

Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 1

Logic Check

Assertion (A): A change of units does not change the number of significant figures in a measurement. Reason (R): Significant figures indicate the precision of measurement, which depends on the least count of the measuring instrument, not on the choice of units.

Reasoning Options

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Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 2

Logic Check

Assertion (A): The trailing zeros in the number 4700 mm (written without a decimal point) are significant. Reason (R): Trailing zeros in a number without a decimal point are not significant according to the rules for significant figures.

Reasoning Options

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Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 3

Logic Check

Assertion (A): The SI is preferred over the CGS and FPS systems for international scientific work. Reason (R): The SI is based on the decimal system, making conversions between multiples and sub-multiples simple, and it is internationally accepted with well-defined unit symbols.

Reasoning Options

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Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 4

Logic Check

Assertion (A): A dimensionally correct equation is always a physically correct equation. Reason (R): Dimensional analysis can detect dimensionless numerical errors in a formula.

Reasoning Options

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Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 5

Logic Check

Assertion (A): A dimensionally wrong equation must be physically wrong. Reason (R): If the dimensions of all terms in an equation are not the same, the equation violates the principle of homogeneity and is therefore incorrect.

Reasoning Options

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Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 6

Logic Check

Assertion (A): The time period of a simple pendulum is independent of the mass of the bob. Reason (R): Dimensional analysis of T = k lˣ gʸ mᶻ gives z = 0, meaning mass does not appear in the expression for T.

Reasoning Options

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Assertion-Reason

Hard difficulty • Check the statement and reason

Hard

Question 7

Logic Check

Assertion (A): In addition or subtraction of measured quantities, the result is rounded to the least number of significant figures among the inputs. Reason (R): In addition or subtraction, the result is rounded to the same number of decimal places as the term with the fewest decimal places.

Reasoning Options

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Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 8

Logic Check

Assertion (A): The radian is the SI unit of plane angle and is a dimensionless quantity. Reason (R): Plane angle is defined as the ratio of arc length to radius; since both have dimensions [L], their ratio is dimensionless.

Reasoning Options

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Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 9

Logic Check

Assertion (A): Dimensional analysis can determine the value of the constant k in the pendulum formula T = k√(l/g). Reason (R): Dimensional analysis determines only the powers of dimensioned physical quantities and cannot find dimensionless constants.

Reasoning Options

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Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 10

Logic Check

Assertion (A): Scientific notation is the best way to report measurements because it removes ambiguity about the number of significant figures. Reason (R): In scientific notation a × 10ᵇ, every digit in the base number a is unambiguously significant, and the power of 10 does not affect the significant-figure count.

Reasoning Options

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Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 11

Logic Check

Assertion (A): The formula K = ma (where m is mass and a is acceleration) can be ruled out as a formula for kinetic energy by dimensional analysis. Reason (R): The dimensions of ma are [M L T⁻²], which do not match the dimensions of kinetic energy [M L² T⁻²].

Reasoning Options

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Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 12

Logic Check

Assertion (A): The number 0.06900 g has four significant figures. Reason (R): The leading zeros are not significant, but the trailing zeros after the decimal point in 0.06900 are significant.

Reasoning Options

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Assertion-Reason

Easy difficulty • Check the statement and reason

Easy

Question 13

Logic Check

Assertion (A): Velocity and speed have the same dimensional formula. Reason (R): Both velocity and speed are defined as the ratio of length to time, giving dimensions [M⁰ L T⁻¹] in both cases.

Reasoning Options

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Assertion-Reason

Hard difficulty • Check the statement and reason

Hard

Question 14

Logic Check

Assertion (A): The number 2.745 rounded to three significant figures is 2.75. Reason (R): When the digit to be dropped is exactly 5 and the preceding digit is even, the preceding digit is left unchanged and the 5 is dropped.

Reasoning Options

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Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 15

Logic Check

Assertion (A): The factor 2 in the formula s = 2πr is treated as having infinite significant figures. Reason (R): Multiplying or dividing factors that are exact numbers (not rounded or measured) have an infinite number of significant digits.

Reasoning Options

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Assertion-Reason

Hard difficulty • Check the statement and reason

Hard

Question 16

Logic Check

Assertion (A): Subtraction of nearly equal measured quantities greatly reduces the number of significant figures in the result. Reason (R): In subtraction, the absolute uncertainties of the two measurements add, while the result (difference) is much smaller, increasing the relative error dramatically.

Reasoning Options

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Assertion-Reason

Hard difficulty • Check the statement and reason

Hard

Question 17

Logic Check

Assertion (A): The SI unit of luminous intensity is the candela (cd). Reason (R): The candela is defined using the Planck constant h and the Boltzmann constant k.

Reasoning Options

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Assertion-Reason

Hard difficulty • Check the statement and reason

Hard

Question 18

Logic Check

Assertion (A): Dimensional analysis cannot distinguish between work and torque. Reason (R): Both work and torque have the same dimensional formula [M L² T⁻²], even though they are physically distinct quantities.

Reasoning Options

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Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 19

Logic Check

Assertion (A): In the kinematic equation x = x₀ + v₀t + ½at², every term on the right-hand side has dimensions of length. Reason (R): v₀t has dimensions [L T⁻¹][T] = [L], and ½at² has dimensions [L T⁻²][T²] = [L], both equal to the dimension of displacement.

Reasoning Options

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Assertion-Reason

Medium difficulty • Check the statement and reason

Medium

Question 20

Logic Check

Assertion (A): The mole is the SI unit of amount of substance and contains exactly 6.02214076 × 10²³ entities. Reason (R): When using the mole, the type of elementary entity must always be specified.

Reasoning Options

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Chapter sections

Chapter 1: Units and Measurement | Assertion-Reason

Assertion (A): A change of units does not change the number of significant figures in a measurement. Reason (R): Significant figures indicate the precision of measurement, which depends on the least count of the measuring instrument, not on the choice of units.

Assertion (A): The trailing zeros in the number 4700 mm (written without a decimal point) are significant. Reason (R): Trailing zeros in a number without a decimal point are not significant according to the rules for significant figures.

Assertion (A): The SI is preferred over the CGS and FPS systems for international scientific work. Reason (R): The SI is based on the decimal system, making conversions between multiples and sub-multiples simple, and it is internationally accepted with well-defined unit symbols.

Assertion (A): A dimensionally correct equation is always a physically correct equation. Reason (R): Dimensional analysis can detect dimensionless numerical errors in a formula.

Assertion (A): A dimensionally wrong equation must be physically wrong. Reason (R): If the dimensions of all terms in an equation are not the same, the equation violates the principle of homogeneity and is therefore incorrect.

Assertion (A): The time period of a simple pendulum is independent of the mass of the bob. Reason (R): Dimensional analysis of T = k lˣ gʸ mᶻ gives z = 0, meaning mass does not appear in the expression for T.

Assertion (A): In addition or subtraction of measured quantities, the result is rounded to the least number of significant figures among the inputs. Reason (R): In addition or subtraction, the result is rounded to the same number of decimal places as the term with the fewest decimal places.

Assertion (A): The radian is the SI unit of plane angle and is a dimensionless quantity. Reason (R): Plane angle is defined as the ratio of arc length to radius; since both have dimensions [L], their ratio is dimensionless.

Assertion (A): Dimensional analysis can determine the value of the constant k in the pendulum formula T = k√(l/g). Reason (R): Dimensional analysis determines only the powers of dimensioned physical quantities and cannot find dimensionless constants.

Assertion (A): The formula K = ma (where m is mass and a is acceleration) can be ruled out as a formula for kinetic energy by dimensional analysis. Reason (R): The dimensions of ma are [M L T⁻²], which do not match the dimensions of kinetic energy [M L² T⁻²].

Assertion (A): The number 0.06900 g has four significant figures. Reason (R): The leading zeros are not significant, but the trailing zeros after the decimal point in 0.06900 are significant.

Assertion (A): Velocity and speed have the same dimensional formula. Reason (R): Both velocity and speed are defined as the ratio of length to time, giving dimensions [M⁰ L T⁻¹] in both cases.

Assertion (A): The number 2.745 rounded to three significant figures is 2.75. Reason (R): When the digit to be dropped is exactly 5 and the preceding digit is even, the preceding digit is left unchanged and the 5 is dropped.

Assertion (A): The factor 2 in the formula s = 2πr is treated as having infinite significant figures. Reason (R): Multiplying or dividing factors that are exact numbers (not rounded or measured) have an infinite number of significant digits.

Assertion (A): The SI unit of luminous intensity is the candela (cd). Reason (R): The candela is defined using the Planck constant h and the Boltzmann constant k.

Assertion (A): Dimensional analysis cannot distinguish between work and torque. Reason (R): Both work and torque have the same dimensional formula [M L² T⁻²], even though they are physically distinct quantities.

Assertion (A): In the kinematic equation x = x₀ + v₀t + ½at², every term on the right-hand side has dimensions of length. Reason (R): v₀t has dimensions [L T⁻¹][T] = [L], and ½at² has dimensions [L T⁻²][T²] = [L], both equal to the dimension of displacement.

Assertion (A): The mole is the SI unit of amount of substance and contains exactly 6.02214076 × 10²³ entities. Reason (R): When using the mole, the type of elementary entity must always be specified.

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