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Class VII T1U1 Measurement Textbook Solutions
Evaluation
I. CHOOSE THE BEST ANSWER.
1. Which of the following is a derived quantity?
a) mass
b) time
c) area
d) length
Ans: c) area
2. Which of the following is correct?
a) 1L = 1cc
b) 1L = 10 cc
c) 1L = 100 cc
d) 1L = 1000 cc
Ans: d) 1L = 1000 cc
3. SI unit of density is
a) kg/m2
b) kg/m3
c) kg/m
d) g/m3
Ans: b) kg/m3
4. Two spheres have mass and volume in the ratio 2:1. The ratio of their density is
a) 1:2
b) 2:1
c) 4:1
d) 1:4
Ans: b) 2:1
5. Light year is the unit of
a) distance
b) time
c) density
d) Both length and time
Ans: a) distance
II. FILL IN THE BLANKS.
1. Volume of irregularly shaped objects are measured using the law of ______________.
Archimedes.
Ans:
2. One cubic metre is equal to _____________ cubic centimetre.
Ans: 10,00,000 (or) 106
3. Density of mercury is _______________.
Ans: 13,600 Kg/m3 .
4. One astronomical unit is equal to _______.
Ans: 1.496 x 1011m.
5. The area of a leaf can be measured using a ________________________.
Ans: graph sheet.
III. STATE TRUE OR FALSE. IF FALSE, CORRECT THE STATEMENT.
1. The region covered by the boundary of a plane figure is called its volume
Ans: False.
The region covered by the boundary of a 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. A ball of iron floats in mercury.
Ans: True
5. A substance which contains less number of molecules per unit volume is said to be denser.
Ans: False
A substance which contains more number of molecules per unit volume is said to be denser.
IV. MATCH THE FOLLOWING ITEMS.
a.
b.
V. ARRANGE THE FOLLOWING IN CORRECT SEQUENCE.
1. 1L, 100 cc, 10 L, 10 cc
Ans: 10 cc, 100 cc, 1 L, 10 L
2. Copper, Aluminium, Gold, Iron
Ans: Aluminium, Iron, Copper, Gold
VI. USE THE ANALOGY TO FILL IN THE BLANK
1. Area : m2 :: Volume : _________
m3
2. Liquid : Litre :: Solid : _________
Kilogram
3. Water : Kerosene :: _______ : Aluminium
Copper
VII. CONSIDER THE FOLLOWING STATEMENTS AND CHOOSE THE CORRECT OPTION.
a. Both assertion and reason are true and reason is the correct explanation of
assertion.
b. Both assertion and reason are true, but reason is not the correct explanation of
assertion.
c. Assertion is true but reason is false.
d. 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: a. 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: b. 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: b. If both assertion and reason are true, but reason is not the correct explanation of assertion
VIII. ANSWER VERY BRIEFLY.
1. Name some of the derived quantities.
Volume, Density,Area are some of the derived quantities.
2. Give the value of one light year.
One light year = 9.46 x 1015m
3. Write down the formula used to find the volume of a cylinder.
Volume of a Cylinder = πr2h
4. Give the formula to find the density of objects.
Density D = mass (m) / Volume (v)
D = m / V
5. Name the liquid in which iron ball sinks.
Water.
As the density of water is less than that of the iron, iron balls sink in water.
6. Name the units used to measure the distance between celestial objects.
Astronomical units and light years are the units used to measure the distance between the celestial objects.
7. What is the density of gold?
The density of gold is 19,300 Kg/m3.
IX. ANSWER BRIEFLY.
1. What are derived quantities?
The 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.
3. Define the density of objects.
The mass of the substance contained in unit volume is known as density.
Density (D) = Mass (M)/ Volume (V)
= M/ V
4. What is one light year?
The distance travelled by light in vacuum during the period of one year is called the light year.
1 Light year = 9.46 × 1015 m
5. Define - Astronomical unit.
The average distance between the earth and the sun is known as the Astronomical unit.
1 AU = 149.6 million km
X. ANSWER IN DETAIL.
1. Describe the graphical method to find the area of an irregularly shaped plane figure.
We can find the area of irregularly shaped plane figures with the help of a graph sheet.
⛯Take a leaf, place it on a graph sheet and draw the outline of the leaf with a pencil. ⛯Remove the leaf.
⛯Count the number of whole squares enclosed within the outline of the leaf.
Take it as M.
⛯Count the number of squares that are more than half. Take it as N.
⛯Count the number of squares which are half of a whole square. Note it as P.
⛯Finally, count the number of squares that are less than half. Let it be Q.
⛯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.
2. How will you determine the density of a stone using a measuring jar?
⛯Take a measuring cylinder and pour some water into it (Do not fill the cylinder completely).
⛯Note down the volume of water from the readings of the measuring cylinder.
⛯Take it as V1. Now take a small stone and tie it with a thread.
⛯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.
⛯Now, the level of water will raise.
⛯Note down the volume of water and take it as V2. T
⛯he volume of the stone is equal to the raise in the volume of water.
Volume of stone = V2 – V1
By this method, we can determine the density of a stone using a measuring jar.
XI. Question based higher order thinking skills:
1. There are three spheres A,B,C as shown below.
Sphere A Sphere B Sphere C
Sphere A and B are made of the same material. Sphere C is made of a different material. Sphere A and C have equal radii. The radius of sphere B is half that of A. Density of A is double that of C.
(i) Find the ratio of masses of spheres A and B
Ratio of masses of sphere A and B
MA : MB
D x VA : D x VB
Mass of sphere A = MA
Mass of sphere B = MB
Mass = Density x Volume
MA = DA x VA
MB = DB x VB (Density is same)
Volume of sphere A = 4/3 πr 3
Volume of sphere B = 4/3 πx ( rA/2 ) x 3
D x 4/3 πr3 : 4/3 π x ( rA/2 ) x 3
= 1 : 1/8 = 8 : 1
(ii) Find the ratio of volumes of sphere A and B
Ratio of volume of spheres A and B
VA : VB
8 : 1
(iii) Find the ratio of masses of spheres A and C
MA : MC
2D x V : D x V ( Density of a A is double that of c)
2 : 1
XII. Numerical Problems:
1. A circular disc has a radius 10 cm. Find the area of the disc in m2. (use π = 3.14)
Radius = 10 cm = 0.1 m
π= 3.14
Area of a circular disc A = ?
Area of a circle A = πr2
= 3.14 x 0.1 x 0.1
A = 0.0314 m2
2. The dimension of a school play ground 500 m. Find the area of the ground.
The dimension of a school play ground = l x b
= 800 m x 500 m
Area of the playground A = l x b = 800 x 500 = 4,00,000
Area = 4,00,000 m2
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/m3 and iron 7,800 kg/m3.
Density of copper Dcu = 8900 kg/m3
Density of iron Dfe = 7800 kg/ m3
Volume of copper sphere = Volume of iron sphere
To find Ratio of masses of copper (Mcu) and Iron (Mfe)
Mass = Density x Volume
Mcu = Dcu x V,
Mfe = Dfe x V
Mcu = 8900 V,
Mfe = 7800 V
Mcu = Mfe
8900 V : 7800 V
1.14 : 1
Ratio between 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 of a liquid M = 250 g
Volume V = 1000 cc
Density of the liquid D =?
Density D = Mass (m) / Volume (v)
= 250 /1000 = 0.25 g/cc
Density of the liquid = 0.25 g/cc.
5. Sphere of radius of 1 cm is made from silver. If the mass of the sphere is 33g, Find the density of silver. ( Take π= 3.14)
Radius of a sphere r = 1 cm
Volume of the sphere V = ?
Mass of the sphere M = 33g
Density of silver D = ?
Density D = mass of the sphere (M) / Volume of the sphere (V)
Volume (V) = 4/3 πr3
= 4/3 x 3.14 x 1 x 1 x 1 = 4.187 (cm3)
D = M/V
= 33/ 4.187
Density of silver sphere = 7.889 g/cc
