Chapter 1 Physical Quantities and Measurements Solved Exercise

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MCQ 1

Statement: The instrument most suitable for measuring the thickness of a few sheets of cardboard is:
Options:
(a) Metre rule
(b) Measuring tape
(c) Vernier Callipers
(d) Micrometer screw gauge
Answer: (d) Micrometer screw gauge
Explanation: A micrometer screw gauge is specifically designed to measure very small thicknesses, such as the thickness of thin materials like sheets of cardboard, with high precision.

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MCQ 2

Statement: One femtometre is equal to:
Options:
(a) 10⁻⁹ m
(b) 10¹⁵ m
(c) 10⁻¹⁵ m
(d) 10⁵ m
Answer: (c) 10⁻¹⁵ m
Explanation: A femtometre (fm) is a unit of length equal to 10⁻¹⁵ metres, commonly used in nuclear physics to measure distances at the subatomic level.

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MCQ 3

Statement: A light year is a unit of:
Options:
(a) Light
(b) Time
(c) Distance
(d) Speed
Answer: (c) Distance
Explanation: A light year is the distance that light travels in one year in a vacuum, which is approximately 9.46×10¹² kilometers.

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MCQ 4

Statement: Which one is a non-physical quantity?
Options:
(a) Distance
(b) Density
(c) Colour
(d) Temperature
Answer: (c) Colour
Explanation: Colour is a perceptual property and not a measurable physical quantity like distance, density, or temperature.

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MCQ 5

Statement: When using a measuring cylinder, one precaution to take is to:
Options:
(a) Check for the zero error
(b) Look at the meniscus from below the level of the water surface
(c) Take several readings by looking from more than one direction
(d) Position the eye in line with the bottom of the meniscus
Answer: (d) Position the eye in line with the bottom of the meniscus
Explanation: To ensure accurate readings, the observer must position their eye level with the bottom of the meniscus, which is the curved surface of the liquid.

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MCQ 6

Statement: Volume of water consumed by you per day is estimated in:
Options:
(a) Millilitre
(b) Litre
(c) Kilogram
(d) Cubic metre
Answer: (b) Litre
Explanation: The volume of water consumption is typically measured in litres, which is a convenient unit for daily use.

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MCQ 7

Statement: A displacement can is used to measure:
Options:
(a) Mass of a liquid
(b) Mass of a solid
(c) Volume of a liquid
(d) Volume of a solid
Answer: (d) Volume of a solid
Explanation: A displacement can is used to measure the volume of an irregularly shaped solid by observing the amount of liquid it displaces.

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MCQ 8

Statement: Two rods with lengths 12.321 cm and 10.3 cm are placed side by side, the difference in their lengths is:
Options:
(a) 2.02 cm
(b) 2.0 cm
(c) 2.021 cm
(d) 2.021 cm
Answer: (b) 2.0 cm
Explanation: The difference in length is calculated as 12.321−10.3=2.021, but the result is rounded off to 2.02.0 cm based on the significant figures.

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MCQ 9

Statement: Which of the following measures are likely to represent the thickness of a sheet of this book?
Options:
(a) 6×10⁻⁵⁶ m
(b) 1×10⁻⁴¹ m
(c) 1.2×10⁻¹⁵ m
(d) 4×10⁻²⁴ m
Answer: (b) 1×10⁻⁴¹ m
Explanation: The thickness of a sheet of paper in a book is typically in the range of 10⁻⁴ meters, equivalent to 0.1 mm.

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1.1 Can a non-physical quantity be measured? If yes, then how?

No, a non-physical quantity, such as emotions, feelings, or color, cannot be measured directly because they are not tangible. However, we can assess them indirectly through surveys, psychological methods, or other qualitative approaches.

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1.2 What is measurement? Name its two parts.

Measurement is the process of comparing an unknown quantity with a standard quantity of the same kind. The two parts of a measurement are:

1. Numerical value (indicates the magnitude).
2. Unit (specifies the standard of measurement, e.g., meters, kilograms).

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1.3 Why do we need a standard unit for measurements?

We need standard units to ensure consistency, reliability, and uniformity in measurements. Without standard units, comparing and sharing results across different places or systems would become difficult and confusing.

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1.4 Write the names of three base quantities and three derived quantities.

Base quantities:

1. Length
2. Mass
3. Time

Derived quantities:

1. Speed (derived from length/time)
2. Volume (derived from length³)
3. Force (derived from mass × acceleration).

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1.5 Which SI unit will you use to express the height of your desk?

The height of a desk is typically expressed in meters (m) or centimeters (cm), depending on its size.

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1.6 Write the names and symbols of all SI base units.

1. Length: Meter (m)
2. Mass: Kilogram (kg)
3. Time: Second (s)
4. Electric current: Ampere (A)
5. Temperature: Kelvin (K)
6. Amount of substance: Mole (mol)
7. Luminous intensity: Candela (cd)

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1.7 Why is a prefix used? Name three sub-multiples and three multiples with their symbols.

Why prefixes are used: Prefixes are added to SI units to express very large or very small quantities in a convenient way, avoiding the need for many zeros.

Sub-multiples:

1. Milli (m) = 10⁻³
2. Micro (µ) = 10⁻⁶
3. Nano (n) = 10⁻⁹

Multiples:

1. Kilo (k) = 10³
2. Mega (M) = 10⁶
3. Giga (G) = 10⁹

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1.8 What is meant by:

(a) 55 pm = 5×10⁻¹² meters (picometers, used to measure atomic distances).
(b) 1515 ns = 15×10⁻⁹ seconds (nanoseconds, used for time intervals in electronics).
(c) 66 µm = 6×10⁻⁶ meters (micrometers, used for measuring microscopic distances).
(d) 55 fs = 5×10⁻¹⁵ seconds (femtoseconds, used in ultrafast phenomena).

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1.9 For what purpose is a Vernier Callipers used?

A Vernier Callipers is used to measure:

1. The external dimensions of an object (e.g., diameter of a cylinder).
2. The internal dimensions of an object (e.g., diameter of a hole).
3. The depth of an object.

Main parts:

• Main scale
• Vernier scale

How least count is found:
The least count is calculated as: Least count=Smallest division on main scale/Total number of divisions on Vernier scale

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1.10 State least count and Vernier scale reading as shown in the figure and hence find the length.

Least count: Assume the smallest division on the main scale is 1 mm and there are 10 divisions on the Vernier scale. Least count=110=0.1 mm

Vernier scale reading: Check the alignment of the Vernier and main scale; the reading will be calculated as: Length=Main scale reading+(Vernier division×Least count).

(Values can be estimated based on the image provided.)

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1.11 Which reading out of A, B, and C shows the correct length and why?

The correct length is the one where the zero of the Vernier scale aligns perfectly with the reading on the main scale. (Specific answer depends on analyzing the given figure in detail.)

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C.1.1 In what unit will you express each of the following?

(a) Thickness of a five-rupee coin:
The thickness of a coin is small, so it is best measured in millimeters (mm) or micrometers (µm) for greater precision.

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(b) Length of a book:
The length of a book can be expressed in centimeters (cm) or millimeters (mm), depending on the level of detail required.

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(c) Length of a football field:
A football field is large, so its length is expressed in meters (m) or sometimes in yards (if using non-metric units).

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(d) The distance between two cities:
The distance between two cities is usually measured in kilometers (km) because the distance is large.

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(e) Mass of a five-rupee coin:
The mass of a coin is small, so it is measured in grams (g) or milligrams (mg) for high precision.

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(f) Mass of your school bag:
The mass of a school bag is measured in kilograms (kg) because it is heavier than smaller objects like a coin.

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(g) Duration of your class period:
The duration of a class period is expressed in minutes (min) or hours (h).

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(h) Volume of petrol filled in the tank of a car:
The volume of petrol is expressed in litres (L), which is the standard unit for liquid volumes.

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(i) Time to boil one litre of milk:
The time to boil milk is usually measured in minutes (min) or seconds (s), depending on how precise the timing is.

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