Measurement — Exercise Solutions
Comprehensive solutions for TN State Board Class 7 Science Term 1 Chapter 1: Measurement. Covers MCQs, fill in the blanks, true/false, match the following, analogy, assertion-reason, very short answers, short answers, detailed answers, numerical problems, and HOTS.
I. Choose the Appropriate Answer (MCQ)
Q1. Which is a derived unit?
(a) mass (b) time (c) area ✓ (d) length
Q2. Which is correct?
(a) 1L = 1 cc (b) 1L = 10 cc (c) 1L = 100 cc (d) 1L = 1000 cc ✓
Q3. SI unit of density is:
(a) kg/m² (b) kg/m³ ✓ (c) kg/m (d) g/m³
Q4. Two spheres have equal mass and volume ratio 2:1. The ratio of their density is:
(a) 1:2 (b) 2:1 ✓ (c) 4:1 (d) 1:4
Q5. Light year is the unit of:
(a) Distance ✓ (b) time (c) density (d) both length and time
Additional MCQs
Q6 (Additional). Unit of volume is:
(a) m³ ✓ (b) m² (c) cm³ (d) km
Q7 (Additional). Physical quantities are classified into ___ types:
(a) three (b) two ✓ (c) four (d) none
Q8 (Additional). SI unit of speed is:
(a) m/s² (b) m/s ✓ (c) km/h (d) m²/s
Q9 (Additional). 1 litre = ___ cc:
(a) 100 (b) 1000 ✓ (c) 10 (d) 0.1
Q10 (Additional). Area of a rectangle formula:
(a) l × b ✓ (b) side × side (c) πr² (d) none
Q11 (Additional). Which is a derived quantity?
(a) length (b) mass (c) time (d) area ✓
Q12 (Additional). Space occupied by a 3D object is:
(a) density (b) volume ✓ (c) area (d) mass
Q13 (Additional). Maximum liquid a container can hold is:
(a) area (b) volume (c) capacity ✓ (d) density
Q14 (Additional). Shortest Earth–Sun distance is called:
(a) light year (b) normal (c) Perihelion ✓ (d) Aphelion
Q15 (Additional). Largest Earth–Sun distance is called:
(a) normal (b) perihelion (c) Aphelion ✓ (d) none
II. Fill in the Blanks
1. Volume of irregularly shaped objects are measured using the law of Archimedes. 2. One cubic metre is equal to 10,00,000 (10⁶) cubic centimetre. 3. Density of mercury is 13,600 kg/m³. 4. One astronomical unit is equal to 1.496 × 10¹¹ m. 5. The area of a leaf can be measured using a graph sheet.
Additional Fill in the Blanks
6. Materials with higher density are called denser. 7. Materials with lower density are called rarer. 8. Area of irregularly shaped figures is calculated using a graph sheet. 9. SI unit of volume is cubic metre (m³). 10. CGS unit of density is g/cm³. 11. If density of solid < density of liquid, it floats. 12. If density of solid > density of liquid, it sinks. 13. Total seconds in one year = 3.153 × 10⁷. 14. Average Earth–Sun distance ≈ 149.6 million km.
III. True or False (with corrections)
Q1. The region covered by the boundary of a plane figure is called its volume.
False. The region covered by the boundary of a plane figure is called its area. Volume refers to the space occupied by a 3D object.
Q2. Volume of liquids can be found using measuring containers.
True.
Q3. Water is denser than kerosene.
True. Water has density 1000 kg/m³, while kerosene has about 800 kg/m³.
Q4. A ball of iron floats in mercury.
True. Iron (7,874 kg/m³) is less dense than mercury (13,600 kg/m³), so an iron ball floats in mercury.
Q5. A substance with fewer molecules per unit volume is said to be denser.
False. A substance with more molecules per unit volume is said to be denser.
Additional True/False
Q6. One square metre is the area inside a square of side 2 m.
False. One square metre is the area inside a square of side 1 metre.
Q7. Area is a derived quantity obtained by multiplying the fundamental quantity length twice.
True. Area = length × length = m², which is derived from the fundamental quantity length.
Q8. Density of water is 100 kg/m³.
False. Density of water is 1000 kg/m³ (or 1 g/cm³).
Q9. Density = mass per unit volume.
True.
Q10. Lightness or heaviness of a body is due to volume.
False. Lightness or heaviness is due to density.
IV. Match the Following
Set 1:
| Column I | Column II | Answer |
|---|---|---|
| i. Area | (a) light year | i → c (m²) |
| ii. Distance | (b) m³ | ii → a (light year) |
| iii. Density | (c) m² | iii → e (kg/m³) |
| iv. Volume | (d) kg | iv → b (m³) |
| v. Mass | (e) kg/m³ | v → d (kg) |
Set 2:
| Column I | Column II | Answer |
|---|---|---|
| i. Area | (a) g/cm³ | i → e (plane figures) |
| ii. Length | (b) measuring jar | ii → d (rope) |
| iii. Density | (c) amount of a substance | iii → a (g/cm³) |
| iv. Volume | (d) rope | iv → b (measuring jar) |
| v. Mass | (e) plane figures | v → c (amount of a substance) |
Set 3 (Additional): Fundamental quantities and units:
| Quantity | Unit |
|---|---|
| 1. Length | (c) metre |
| 2. Time | (d) second |
| 3. Mass | (e) kilogram |
| 4. Temperature | (b) kelvin |
| 5. Electric current | (a) ampere |
V. Arrange in Correct Sequence
Q1. Arrange in ascending order: 1L, 100 cc, 10 L, 10 cc
Q2. Arrange metals in ascending order of density: Copper, Aluminium, Gold, Iron
VI. Analogy
Q1. Area : m² :: Volume : m³
Q2. Liquid : Litre :: Solid : cm³
Q3. Water : Kerosene :: Iron : Aluminium (water is denser than kerosene; iron is denser than aluminium)
VII. Assertion and Reason
Q1. Assertion: Volume of a stone is found using a measuring cylinder. Reason: Stone is an irregularly shaped object.
Q2. Assertion: Wood floats in water. Reason: Water is a transparent liquid.
Q3. Assertion: Iron ball sinks in water. Reason: Water is denser than iron.
Additional Assertion and Reason
Q4. Assertion: Distance between celestial bodies is measured in light years. Reason: Distance light travels in one year in vacuum is one light year.
Q5. Assertion: It is easier to swim in sea water than river water. Reason: Density of sea water exceeds that of river water.
VIII. Very Short Answer Questions
Q1. Name some derived quantities.
Area, volume, density, speed, velocity, acceleration.
Q2. What is the value of one light year?
1 light year = 9.46 × 10¹⁵ m
Q3. Write the formula for volume of a cylinder.
V = πr²h, where r is radius and h is height.
Q4. Write the formula for density.
Density = Mass / Volume (D = M/V)
Q5. Name the liquid in which an iron ball sinks.
An iron ball sinks in water because the density of iron (7,874 kg/m³) exceeds that of water (1,000 kg/m³).
Q6. Which unit is used to measure distance between celestial objects?
Astronomical unit (AU) and light year.
Q7. What is the density of gold?
19,300 kg/m³
Additional Very Short Answers
Q8. What is the SI unit of speed?
m/s (metre per second)
Q9. What is the fundamental unit of amount of substance?
Mole (mol)
Q10. What are the types of physical quantity?
Fundamental quantity and derived quantity.
Q11. What is the SI unit of electric charge?
Coulomb (C)
Q12. Formula for area of a circle?
A = πr²
Q13. How to find area of irregularly shaped figures?
Graphical method using a graph sheet.
Q14. How to determine volume of a liquid?
Using a measuring cylinder or measuring jar.
Q15. Which has more volume — iron block or wooden block of same mass?
Wooden block (wood has lower density, so it occupies more volume for the same mass).
Q16. Which has more density — water or cooking oil?
Water (1,000 kg/m³) is denser than cooking oil (~900 kg/m³).
IX. Short Answer Questions
Q1. What are derived quantities? Give examples.
Derived quantities are physical quantities obtained by multiplying, dividing, or mathematically combining fundamental quantities. Examples: area (length × length), volume (length × length × length), density (mass/volume), speed (distance/time).
Q2. Distinguish between volume of liquid and capacity of a container.
| Volume of Liquid | Capacity of Container |
|---|---|
| Space taken up by a liquid | Ability to hold a substance |
| Measured in cubic units (m³, cm³) | Measured in litres, gallons, etc. |
| Calculated from dimensions | Measured using calibrated containers |
Q3. Define density.
Density is the mass of a substance contained in unit volume. Formula: D = M/V, where D is density, M is mass, and V is volume. SI unit: kg/m³.
Q4. What is one light year?
One light year is the distance light travels in vacuum during one year. 1 light year = 9.46 × 10¹⁵ m. It is used to measure distances between stars and other celestial objects.
Q5. Define one astronomical unit.
One astronomical unit (AU) is the average distance between the Earth and the Sun. 1 AU = 1.496 × 10¹¹ m. It is used for measuring distances within the solar system.
Additional Short Answers
Q6. What is a fundamental quantity? Give examples.
A fundamental quantity is a physical quantity that cannot be expressed in terms of other quantities. Examples: length, mass, time, temperature, electric current, amount of substance, and luminous intensity.
Q7. Define mass and its unit.
Mass is the amount of matter contained in a body. Its SI unit is kilogram (kg).
Q8. What are multiples and sub-multiples of mass?
Multiples: quintal (1 quintal = 100 kg), metric tonne (1 tonne = 1000 kg). Sub-multiples: gram (1 g = 10⁻³ kg), milligram (1 mg = 10⁻⁶ kg).
Q9. What is a physical quantity?
A physical quantity is any quantity that can be measured. Examples: length of cloth, mass of a brick, time of travel.
Q10. What is a 'unit'?
A unit is the known fixed quantity used as a standard of measurement for a physical quantity. For example, metre is the unit of length.
Q11. What is measurement?
Measurement is the comparison of an unknown quantity with a standard or known quantity (unit) of the same kind.
Q12. What is area?
Area is the measure of the region enclosed within the boundary of a plane (two-dimensional) figure.
Q13. What is capacity of a container?
Capacity is the volume of liquid a container can hold. It is measured in litres, millilitres, gallons, etc.
Q14. State the relation between density, volume, and mass.
Density = Mass / Volume. From this: Mass = Density × Volume, and Volume = Mass / Density.
X. Detailed Answer Questions
Q1. Explain the graphical method to find the area of an irregularly shaped plane figure.
1. Place the irregularly shaped object on graph paper and trace its outline carefully. 2. Count the number of complete squares inside the outline (M). 3. Count the squares that are more than half inside the outline (N). 4. Count the half squares (P). 5. Count the squares that are less than half inside the outline (Q).
Area = M + (¾)N + (½)P + (¼)Q square cm
This method provides a good approximation for the area of any irregular shape.
Q2. Describe how to determine the density of a stone using a measuring jar.
1. Find the mass of the stone using a physical balance. Let the mass be 'm' grams. 2. Pour water into a measuring cylinder and record the initial volume (V₁). 3. Tie the stone with a thread and gently lower it into the water until fully immersed, ensuring it does not touch the walls. 4. Record the new water level (V₂). 5. Volume of stone = V₂ − V₁. 6. Density = Mass / Volume = m / (V₂ − V₁).
Example: If mass = 50 g, V₁ = 40 cm³, V₂ = 60 cm³, then Volume = 20 cm³ and Density = 50/20 = 2.5 g/cm³.
XI. Numerical Problems
Q1. A circular disc has radius 10 cm. Find its area in m². (π = 3.14)
- r = 10 cm = 0.1 m
- A = πr² = 3.14 × 0.1 × 0.1 = 0.0314 m²
Q2. A playground has dimensions 800 m × 500 m. Find its area.
- A = l × b = 800 × 500 = 4,00,000 m²
Q3. Two spheres of the same size, one of copper (8,900 kg/m³) and one of iron (7,800 kg/m³). Find the ratio of their masses.
- Same volume, so mass ratio = density ratio
- m_copper / m_iron = 8900V / 7800V = 8900 : 7800 = 89 : 78 ≈ 1.14 : 1
Q4. A liquid has mass 250 g and volume 1000 cc. Find its density.
- D = M/V = 250/1000 = 0.25 g/cm³
Q5. A silver sphere of radius 1 cm has mass 33 g. Find its density. (π = 3.14)
- V = (4/3)πr³ = (4/3)(3.14)(1)³ = 4.186 cm³
- D = M/V = 33/4.186 = 7.889 g/cm³
Q6 (Additional). An iron piece weighs 230 g and has volume 20 cm³. Find its density.
- D = M/V = 230/20 = 11.5 g/cm³
Q7 (Additional). Find the mass of silver with volume 50 cm³ and density 10.5 g/cm³.
- M = D × V = 10.5 × 50 = 525 g
XII. Higher Order Thinking Skills (HOTS)
(i) Ratio of masses A : B
Since A and B share the same density (same material), mass ratio equals volume ratio.
- V_A = (4/3)πr³; V_B = (4/3)π(r/2)³ = (1/8) of V_A
- Ratio = 8 : 1
(ii) Ratio of volumes A : B
8 : 1 (since radius of B is half of A, volume ratio is (r)³ : (r/2)³ = 8 : 1)
(iii) Ratio of masses A : C
Same radius means same volume. Mass = Density × Volume.
- Density of A = 2 × Density of C, so M_A = 2 × M_C
- Ratio = 2 : 1
HOTS: Why does an iron needle sink in water but not an iron ship?
An iron needle is compact with density 7.6 g/cm³ (greater than water's 1 g/cm³), so it sinks. A ship is mostly hollow inside, making its overall volume much larger relative to its mass. The effective density of the ship falls below 1 g/cm³, allowing it to float by displacing a volume of water equal to its own weight (Archimedes' principle).
XIII. Crossword Puzzle Answers
Across: 1. KELVIN (SI unit of temperature) 2. VOLUME (a derived quantity) 3. DENSITY (mass per unit volume) 4. CAPACITY (maximum volume of liquid a container can hold)
Down: a. VELOCITY (a derived quantity) b. CUBIC METRE (SI unit of volume) c. MERCURY (a liquid denser than iron) d. LIGHT YEAR (unit of length for very long distances)
Common Mistakes to Avoid
1. Confusing area and volume — Area is 2D (m²); volume is 3D (m³). Do not interchange their units. 2. Mixing up fundamental and derived quantities — Length, mass, and time are fundamental; area, volume, and density are derived from them. 3. Forgetting unit conversions — 1 m = 100 cm, so 1 m² = 10,000 cm², and 1 m³ = 10,00,000 cm³. Always convert before calculating. 4. Saying density = volume/mass — The correct formula is Density = Mass/Volume (D = M/V), not the other way around. 5. Confusing mass and weight — Mass is the amount of matter in a body (kg); weight is the gravitational force on that mass (N). 6. Mixing up astronomical unit and light year — AU measures distances within the solar system; light year measures distances between stars. 7. Assuming heavier objects always sink — Whether an object floats depends on its density relative to the liquid, not just its mass. An iron ball floats in mercury because mercury is denser.
Exam Checklist
- [ ] Can define fundamental and derived quantities with examples
- [ ] Can list all 7 SI fundamental quantities and their units
- [ ] Can calculate area of rectangle, triangle, and circle
- [ ] Can calculate volume of cube, cuboid, cylinder, and sphere
- [ ] Can explain the graphical method for area of irregular shapes
- [ ] Can define density and use D = M/V for numerical problems
- [ ] Can describe the water displacement method for finding volume of irregular objects
- [ ] Know the difference between volume and capacity
- [ ] Can define astronomical unit and light year with their values
- [ ] Can solve numerical problems on density, area, and volume
- [ ] Can explain why objects float or sink based on density comparison