Chapter 1: Units and Measurement Short Questions | physics Class 11 CBSE

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Chapter 1: Units and Measurement Short Questions | physics Class 11 CBSE | ByteNotes.in

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Question 1

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What is a unit of measurement? Why do we need a standard unit?

A unit is a certain basic, arbitrarily chosen, internationally accepted reference standard used to express the result of any measurement of a physical quantity.
Without a standard unit, measurements made by different observers or in different countries would be inconsistent and incomparable.
The result of a measurement is always expressed as a number accompanied by the unit, making both components essential for a complete physical statement.

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Question 2

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Distinguish between fundamental units and derived units with one example each.

Fundamental (base) units are the units of base quantities that are chosen as independent standards; for example, the metre (unit of length) is a fundamental unit.
Derived units are formed by combining base units through multiplication or division according to the defining equation of the quantity; for example, m s⁻¹ is the derived unit of velocity.
A complete set of both base units and derived units constitutes a system of units, such as the SI system.

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Question 3

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Name the seven base quantities of the SI system and their corresponding SI units.

The seven base quantities are: length (metre, m), mass (kilogram, kg), time (second, s), electric current (ampere, A), and thermodynamic temperature (kelvin, K).
The remaining two are amount of substance (mole, mol) and luminous intensity (candela, cd), completing the seven SI base units.
Each base unit is defined precisely using fundamental physical constants, ensuring universality and reproducibility of measurements worldwide.

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Question 4

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What are the CGS, FPS, and MKS systems of units? State their base units for length, mass, and time.

In the CGS system the base units are centimetre (length), gram (mass), and second (time); in the FPS system they are foot, pound, and second.
In the MKS system the base units are metre, kilogram, and second — the same base quantities as SI but defined less precisely than the modern SI.
All three systems were used extensively before the SI was internationally adopted, and they illustrate the need for a single globally accepted system.

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Question 5

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What is the SI unit of plane angle and solid angle? Are they dimensional quantities?

The SI unit of plane angle dθ is the radian (rad), defined as the ratio of the arc length ds to the radius r of the circle.
The SI unit of solid angle dΩ is the steradian (sr), defined as the ratio of the intercepted spherical surface area dA to the square of the radius r.
Both radian and steradian are dimensionless quantities because they are ratios of like physical quantities (length/length and area/area respectively).

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Question 6

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State the rules for identifying significant figures in a measured value.

All non-zero digits are significant, and all zeros between two non-zero digits are significant regardless of the position of the decimal point.
Leading zeros (zeros to the left of the first non-zero digit in a number less than 1) are never significant, whereas trailing zeros in a number with a decimal point are significant.
Trailing zeros in a whole number without a decimal point are not significant; scientific notation eliminates all ambiguity about trailing zeros.

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Question 7

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How does a change of units affect the number of significant figures in a measurement?

A change of units does not change the number of significant figures in a measurement; the precision of measurement is an intrinsic property of the data.
For example, 2.308 cm has four significant figures, and the same length written as 0.02308 m or 23.08 mm still has four significant figures.
This is because significant figures reflect the reliability of the measuring instrument, not the choice of units used to express the value.

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Question 8

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What is scientific notation? What advantage does it offer in expressing measurements?

Scientific notation expresses any number as a × 10ᵇ, where a is a number between 1 and 10 and b is any integer exponent, for example 4.700 × 10² cm.
It removes all ambiguity about trailing zeros: every zero appearing in the base number a is always significant in scientific notation.
It also simplifies the expression of very large or very small quantities and gives a direct indication of the order of magnitude of the physical quantity.

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Question 9

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State the rule for significant figures in multiplication and division of measured quantities.

In multiplication or division, the final result should retain as many significant figures as are present in the original number that has the least number of significant figures.
For example, if mass = 4.237 g (4 sig. figs.) and volume = 2.51 cm³ (3 sig. figs.), the density must be reported to only 3 significant figures as 1.69 g cm⁻³.
This rule ensures the result does not claim greater precision than the least precise input measurement on which it is based.

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Question 10

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State the rule for significant figures in addition and subtraction of measured quantities.

In addition or subtraction, the final result should retain as many decimal places as are present in the number with the least number of decimal places.
For example, adding 436.32 g, 227.2 g, and 0.301 g gives 663.821 g by arithmetic, but since 227.2 g has only one decimal place, the result must be rounded to 663.8 g.
This rule is different from the multiplication rule and is expressed in terms of decimal places, not total significant figures.

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Question 11

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State the rounding-off convention used when the digit to be dropped is exactly 5.

When the insignificant digit to be dropped is exactly 5, the preceding digit is examined: if it is even, the digit 5 is simply dropped leaving the preceding digit unchanged.
If the preceding digit is odd, it is raised by 1 when the 5 is dropped; for example, 2.745 rounded to three significant figures becomes 2.74 (preceding digit 4 is even).
This convention, sometimes called the round-half-to-even rule, prevents systematic bias that would arise if 5 were always rounded up.

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Question 12

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What are the dimensions of a physical quantity? How are they denoted?

The dimensions of a physical quantity are the powers (exponents) to which the base quantities are raised to represent that quantity in terms of fundamental quantities.
They are denoted using square brackets; for example, length has dimension [L], mass [M], time [T], electric current [A], temperature [K], luminous intensity [cd], and amount of substance [mol].
In mechanics, all quantities can be expressed in terms of [L], [M], and [T]; for example, the dimension of force is [M L T⁻²].

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Question 13

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Write the dimensional formula for volume, velocity, acceleration, and force.

Volume = [M⁰ L³ T⁰] since it is the product of three lengths; velocity = [M⁰ L T⁻¹] since it is length divided by time.
Acceleration = [M⁰ L T⁻²] since it is change of velocity per unit time, and force = [M L T⁻²] since it equals mass multiplied by acceleration.
In all these formulae, zero exponents indicate that the corresponding base quantity does not appear in the expression for that physical quantity.

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Chapter 1: Units and Measurement | Short Questions

What is a unit of measurement? Why do we need a standard unit?

Distinguish between fundamental units and derived units with one example each.

Name the seven base quantities of the SI system and their corresponding SI units.

What are the CGS, FPS, and MKS systems of units? State their base units for length, mass, and time.

What is the SI unit of plane angle and solid angle? Are they dimensional quantities?

State the rules for identifying significant figures in a measured value.

How does a change of units affect the number of significant figures in a measurement?

What is scientific notation? What advantage does it offer in expressing measurements?

State the rule for significant figures in multiplication and division of measured quantities.

State the rule for significant figures in addition and subtraction of measured quantities.

State the rounding-off convention used when the digit to be dropped is exactly 5.

What are the dimensions of a physical quantity? How are they denoted?

Write the dimensional formula for volume, velocity, acceleration, and force.

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