Lesson 1. Measurement |
Lesson 1. Measurement
I . Choose the correct answer.
1. Which of the following is a derived unit?
- mass
- time
- area
- length
Ans : area
2. Which of the following is correct?
- 1L = 1cc
- 1L = 10 cc
- 1L = 100 cc
- 1L = 1000 cc
Ans : 1L = 1000 cc
3. SI unit of density is
- kg/m^{2}
- kg/m^{3}
- kg/m
- g/m^{3}
Ans : kg/m^{3}
4. Two spheres have equal mass and volume in the ratio 2:1. The ratio of their density is
- 1:2
- 2:1
- 4:1
- 1:4
Ans : 2:1
5. Light year is the unit of
- Distance
- time
- density
- both length and time
Ans : Distance
II. Fill in the blanks:
1. Volume of irregularly shaped objects are measured using the law of ______________.
Ans : Archimedes
2. One cubic metre is equal to _____________ cubic centimetre.
Ans : 100
3. Density of mercury is _______________.
Ans : 13600kg/m^{3}
4. One astronomical unit is equal to ________________________.
Ans : 1.496×10^{11}m
5. The area of a leaf can be measured using a ________________________.
Ans : graphical method
III. State whether the following statements are true or false:
1. The region covered by the boundary of the plane figure is called its volume.
Ans : False
Cu. St. : The region covered by the boundary of the plane figure is called its area.
2. Volume of liquids can be found using measuring containers.
Ans : True
3. Water is denser than kerosene.
Ans : True
4. Aball ofiron floats in mercury.
Ans : True
5. A substance which contains less number of molecules per unit volume is said to be denser.
Ans : False.
Cu. St. : A substance which contains more number of molecules per unit volume is said to be denser.
IV. (1) Match the items
1. Area | light year | ||
2. Distance | m^{3} | ||
3. Density | m^{2} | ||
4. Volume | kg | ||
5. Mass | kg / m^{3} | ||
Ans : 1 – C, 2 – A, 3 – E, 4 – B, 5 – D |
IV. (2) Match the items
1. Area | g / cm^{3} | ||
2. Length | measuring jar | ||
3. Density | amount of a substance | ||
4. Volume | rope | ||
5. Mass | plane figures | ||
Ans : 1 – E, 2 – D, 3 – A, 4 – B, 5 – C |
V. Arrange the following in correct sequence:
1. 1L, 100 cc, 10 L, 10 cc
Ans : 10cc, 100cc, 1L, 10L
2. Copper, Aluminium, Gold, Iron
Ans : Aluminium, Iron, Copper, Gold
VI. Use the analogy to fill in the blank:
1. Area: m^{2} : : Volume: _________
Ans: m^{3}
2. Liquid: Litre : : Solid: _________
Ans : Cubic Metre
3. Water: kerosene : : _______ : Aluminium
Ans : Iron
VII. Assertion and reason type questions:
Mark the correct choice as
- If both assertion and reason are true and reason is the correct explanation of assertion.
- If both assertion and reason are true, but reason is not the correct explanation of assertion.
- Assertion is true but reason is false.
- Assertion is false but reason is true.
1. Assertion : Volume of a stone is found using a measuring cylinder.
Reason : Stone is an irregularly shaped object.
Ans : If both assertion and reason are true and reason is the correct explanation of assertion.
2. Assertion : Wood floats in water.
Reason : Water is a transparent liquid.
Ans : If both assertion and reason are true, but reason is not the correct explanation of assertion.
3. Assertion : Iron ball sinks in water.
Reason : water is denser than iron.
Ans : Assertion is true but reason is false.
VIII. Give very short answer:
1. Name some of the derived quantities.
Area, volume, speed, density.
2. Give the value of one light year.
9.46x 10^{15}m
3. Write down the formula used to find the volume of a cylinder.
πr^{2}h
4. Give the formula to find the density of objects.
Density (D) = Mass (M) / Volume(v)
5. Name the liquid in which an iron ball sinks.
Water
6. Name the units used to measure the distance between celestial objects.
Astronomical unit, Light year
7. What is the density of gold?
19,300 kg/m^{3}
IX. Give short answer :
1. What are derived quantities ?
All other physical quantities which can be obtained by multiplying, dividing or by mathematically combining the fundamental quantities are known as “derived quantities”.
2. Distinguish between the volume of liquid and capacity of a container.
Volume of liquid | Capacity of a container | ||
The volume of any liquid is equal to the space that it fills | The maximum volume of liquid that a container can hold is known as the ‘capacity of container’. |
3. Define the density of objects.
Density of a substance is defined as the mass of the substance contained in unit volume(1 m^{3}).
Density (D) = Mass (M) / Volume(V)
4. What is one light year?
One light year is defined as the distance travelled by light in vacuum during the period of one year.
1 Light year = 9.46 x 10^{15} m.
5. Define – one astronomical unit ?
One astronomical unit is defined as the average distance between the earth and the sun.
1AU = 1.496 x 10^{11}m.
X. Answer in detail.
1. Describe the graphical method to find the area of an irregularly shaped plane figure.
To find the area of an irregular shaped plane figure by the graphical method:
- First take the irregularly shaped leaf.
- Place the leaf on a graph sheet and draw the outline of the leaf with a pencil ( Figure ).
- Remove the leaf.
- You can see the outline of the leaf on the graph sheet.
i. Now, count the number of whole squares enclosed within the outline of the leaf. Take it to be M.
ii. Then, count the number of squares that are more than half. Take it as N.
iii. Next, count the number of squares which are half of a whole squares. Note it to be P.
iv. Finally, count the number of squares that are less than half. Let it be Q.
v. M=52 ; N=12, P=6 ; Q=12
Now, the approximate area of the leaf can be calculated using the following formula :
Approximate area of the leaf | = M + (3/4) N+(1/2)P +(1/4)Q square cm. |
Area of the leaf | = 52 + (3/4) x 12 + (1/2) x 6 + (1/4) x 12 |
=52+9+3+3 | |
Area of the leaf | =67sq.cm |
This formula can be used to calculate the area of any irregularly shaped plane figures.
2. How will you determine the density of a stone using a measuring jar ?
- Take a measuring cylinder and Gr pour some water into it (Do not fill F the cylinder completely).
- Note down the volume of water from the readings of the measuring cylinder.
- Take it as V_{1}
- Now take a small stone and tie it Volume of an irregularly with a thread. shaped object
- Immerse the stone inside the water by holding the thread.
- This has to be done such that the stone does not touch the walls of the measuring cylinder ( Figure ).
- Now, the level of water has raised. Note down the volume of water and take it to be V,.
- The volume of the stone is equal to the raise in the volume of water.
V_{1} | = 30 ml |
V_{2} | = 40 ml |
Volume of stone | = V_{2 }– V_{1} |
Volume of stone | = 40 – 30 = 10 ml |
Mass of stone | 20 gm |
Density of stone | = 20 /10 = 2 gm/cm^{3} |
Xl. Numerical problems :
1. A circular disc has a radius 10cm. Find the area of the disc in m^{2.} (Use 1 =3.14)
r_{1 } | = 10 cm |
Area of a circular disc | = πr^{2} |
= 22 / 7 x 10 x 10 | |
Area of a circular disc | = 314.3m |
2. The dimension of a school playground is 800m x 500m. Find the area of the ground.
Area of a school play ground | = length x breadth |
= 800 x 500 | |
Area of the ground | = 400000 m^{2} |
3. Two spheres of same size are made from copper and iron respectively. Find the ratio between their masses. Density of copper 8,900 kg/m^{3} and iron 7,800 kg/m^{3}.
Mass of copper | = M_{1} |
Density of copper = D_{1} | = 8900 kg/m^{3} |
Volume of copper | = V_{1} |
Mass of iron | = M_{1} |
Density of iron = D_{2} | = 7800 kg/m^{3} |
Volume of iron | =V_{2} |
V_{1} = V_{2 }= V | |
M_{1} | = D_{1 }x V_{1} |
= D_{1 }x V | |
= 8900 x V | |
M_{2} | = D_{2 }x V_{2} |
= 7800 x V | |
M_{1} | = M_{2} |
8900V | = 7800V |
M_{1 }/ M_{2} | 8900V / 7800V = 1.14 / 1 |
M_{1 }: M_{2} | 1.14 : 1 |
Ratio of their masses | = 1.14 : 1 |
4. A liquid having a mass of 250 g fills a space of 1000 cc. Find the density of the liquid.
Mass (M) | =250 g |
Volume (V) | = 1000 cc |
Density of liquid (D) | = ? |
D | = M / V |
= 250 / 1000 = 0.25 | |
D | = 0.25 g/cc |
5. A sphere of radius 1 cm is made from silver. If the mass of the sphere is 33g, find the density of silver. ( Take π = 3.14)
Volume of a silver sphere | = 4/3πr^{3} |
= 4/3 x 22/7 x 1 x 1 x 1 = 88 / 21 | |
Volume of a silver sphere | = 4.2 cm^{3} |
Mass of a sphere (M) | =33 g |
Density of silver (D) | = ? |
D | = M / V |
= 33 / 4.2 = 7.86 | |
Density of silver (D) | = 7.86 g/cc |
XIl. Cross word Puzzle :
CLUES – ACROSS
1. Sl unit of temperature
- Kelvin
2. derived quantity
- Volume
3. Mass per unit volume
- Density
4. Maximum volume of liquid a container can hold
- Capacity
CLUES -DOWN
a. A derived quantity
- Velocity
b. SI Unit of volume
- Cubic metre
c. A liquid denser than iron
- Mercury
d. A unit of length used to measure very long distances
- Light year
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