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Page No 154:
Question 1:
Four liquids have densities as follows:
Liquid A-1.2 g/cm^{3}; Liquid B-13 g/cm^{3}; Liquid C-0.9 g/cm^{3}; Liquid D-29 g/cm^{3}
When poured into a container, which one of these pictures shows the correct arrangement of these liquids?
Figure
Answer:
Figure C shows the correct picture, as in this picture, the liquids are arranged in the correct order of decreasing density.
Page No 154:
Question 2:
What is the density of the oil in this bottle?
(a) 0.9 g/ml
(b) 0.1 g/ml
(c) 1.9 g/ml
(d) 1.1 g/ml
Figure
Answer:
Mass of the oil in the bottle = 450 g
= 0.9 g/ml
Page No 154:
Question 3:
What will be the volume of water that will fill the same bottle? density of water = 1 g/ml
(a) 500 ml
(b) 100 gm
(c) 1000 ml
(d) 980 ml
Answer:
= 500 mL
Page No 155:
Question 4:
The table below gives the mass and volume of three objects (P, Q and R).
P | Q | R | |
Mass in grams | 4 | 8 | 6 |
Volume in cm^{3} | 1 | 10 | 3 |
Which statement about the densities of these three objects is correct?
(a) Q is denser than P.
(b) P is denser than R.
(c) P and R have equal densities.
(d) Q and R have equal densities.
Answer:
P | Q | R | |
Mass in grams | 4 | 8 | 6 |
Volume in cm^{3} | 1 | 10 | 3 |
Density in g/cm^{3} | 4/1=4 | 8/10=0.8 |
6/3=2 |
The statements about the densities of these three objects are as follows.
(a) Q is denser than P - False
(b) P is denser than R - True
(c) P and R have equal densities - False
(d) Q and R have equal densities - False
Page No 155:
Question 5:
A fresh egg sinks in pure water, whereas it floats in salty water. This is because
(a) salt water is denser than pure water.
(b) the egg is less dense than pure water.
(c) salt water is less dense than an egg.
(d) salt water is denser than the egg.
Answer:
(d) salt water is denser than the egg
A fresh egg sinks in pure water, whereas it floats in salty water, because salt water is denser than the egg.
Page No 155:
Question 6:
Select the correct choice from the codes given below the four statements.
A. An orange and a cricket ball of the same size must be of the same mass.
B. A kilogram of iron and a kilogram of cotton have the same mass.
C. A small piece of wood will float on water but a heavy log will sink.
D. A kilogram of sweets taken up in an aeroplane far away from the surface of the earth will become less than a kilogram.
(a) false, true, false, false
(b) false, false, false, false
(c) true, false true, true
(d) true, false, false, true
Answer:
A. False
An orange and a cricket ball that have the same size do not have the same mass as they have different densities.
B. True
C. False
A small piece of wood and a heavy log have approximately the same densities, and so, both will float.
D. False
The mass of an object does not change from place to place.
Page No 155:
Question 7:
A factory manager has to find out how many small packs of biscuits can be put into a large cardboard carton. To calculate this, he needs to know
(a) the mass of the small packs.
(b) the weight of the small packs and the bigger carton.
(c) the volume of one small pack and of the big carton.
(d) the density of the biscuits.
Answer:
(c) the volume of one small pack and that of the big carton.
If a factory manager needs to find out how many small packs of biscuits can be put into a big cardboard carton, then he needs to know the volume of a small pack and that of the big carton.
Page No 155:
Question 8:
The density of water is 1 g/cm^{3}. If each of these liquids X, Y and Z is immiscible in water, which of them will float on water.
Liquid | Mass (g) | Volume (cm^{3}) |
X | 5.4 | 5 |
Y | 46 | 50 |
Z | 130 | 100 |
(a) Liquid Y will float.
(b) Liquid X and Z will float.
(c) All the three liquids will float.
(d) None of them will float on water.
Answer:
The density of water is 1 g/cm^{3}. If each of these liquids X, Y and Z is immiscible in water, then to know which of them will float on water, we need to find their densities using the formula 'Density = Mass / Volume'.
Liquid | Mass (g) | Volume (cm^{3}) | Density (g/cm^{3}) |
X | 5.4 | 5 | 5.4 / 5 = 1.08 |
Y | 46 | 50 | 46 / 50 = 0.9 |
Z | 130 | 100 | 130 / 100 = 1.3 |
(a) True
(b) False
The liquids X and Z are denser than water. Hence they will sink in water.
The liquids X and Z are denser than water. Hence they will sink in water
Liquid Y will float because its density is less than the density of water.
Page No 155:
Question 9:
Liquid A (density-0.71 g/cm^{3}); Liquid B (density-1.2 g/cm^{3}); Liquid C (density-13 g/cm^{3}) are three liquids which do not mix with each other. They are filled in a container as shown here.
Figure
A solid object of density 4 g/cm^{3} is dropped into the liquid. Where will it come to rest?
(a) on top of layer A
(b) in layer B
(c) between layer B and C
(d) at the bottom
Answer:
(c) Between layers B and C
The solid object will come to rest between layers B and C, because its density is greater than the densities of liquid A and B but less than the density of liquid C.
Page No 156:
Question 10:
If the earth's gravitational pull suddenly disappeared (or became zero), the objects on it would:
A. have no weight.
B. have the same mass as earlier.
C. have no mass.
D. have the same weight as earlier.
(a) B and C are correct.
(b) A and B are correct.
(c) C is correct.
(d) D is correct.
Answer:
(b) A and B are correct
If the earth's gravitational pull suddenly disappeared (or became zero), the objects on it would have no weight but have the same mass as earlier.
Page No 156:
Question 11:
Read the following statements. If they are true for mass, write M against them. If they are true for weight, write W.
(a) It is the gravitational force on the body.
(b) It is the quantity of matter in the body.
(c) It will not change from place to place.
(d) It is measured in Newtons.
(e) It remains the same on the surface of the earth and on the surface of the moon.
(f) It will change from place to place.
(g) It is measured with a spring balance.
(h) It is measured in kilograms.
(i) It becomes zero in outer space.
(j) It is measured with a beam balance.
Answer:
(a) It is the gravitational force on the body. W
(b) It is the quantity of matter in the body. M
(c) It will not change from place to place. W
(d) It is measured in newtons. W
(e) It remains the same on the surface of the earth and on the surface of the moon. M
(f) It will change from place to place. W
(g) It is measured with a spring balance. W
(h) It is measured in kilograms. M
(i) It becomes zero in outer space. W
(j) It is measured with a beam balance. M
Page No 156:
Question 12:
What unit would you use for measuring the mass of each of the following:
(a) a loaded truck
(b) a small packet of garam masala
(c) a sack of rice
(d) a tablet of medicine
(e) your school bag loaded with books
(f) the total amount of wheat stored in a warehouse.
(g) a cake of soap
Answer:
(a) a loaded truck - tonnes
(b) a small packet of garam masala - gm
(c) a sack of rice - kg
(d) a tablet of medicine - milligram (mg)
(e) your school bag loaded with books - kg
(f) the total amount of wheat stored in a warehouse - tonnes
(g) a cake of soap - gm
Page No 156:
Question 13:
State whether the following are true or false. Rewrite the false ones correctly.
(a) One kg of oranges and one kg of apples will have the same mass anywhere.
(b) On the moon, you can easily lift a load that weighs 60 kg-wt on earth.
(c) Weight is measured using a beam balance.
(d) Mass is the amount of matter present in a body.
(e) A fully loaded truck has more mass than an empty one.
(f) In space, the mass of a body remains the same as it was on earth, but its weight becomes zero.
Answer:
(a) True
(b) True
(c) False
Weight is measured using a spring balance.
(d) True
(e) True
(f) True
Page No 156:
Question 14:
(a) Write down four differences between mass and weight.
(b) Would you be able to lift a large crate of mass 60 kg on the earth? What would it weigh on the moon? What would be its mass on the moon?
Answer:
(a) Difference between mass and weight-
Mass | Weight |
It is the quantity of matter contained in a body. | Weight is the gravitational force acting on a body. |
It does not change from place to place. | It changes from place to place. |
It is measured in kg and gm. | It is measured in newton. |
It is measured with a beam balance. | It is measured using a spring balance. |
(b) The weight of the large crate on the moon will be one-sixth of its weight on the earth, as the force of gravity on the moon is one-sixth that on the earth. But its mass remains the same on the moon.
Page No 156:
Question 15:
Find the densities of these substances from the given data. The make a list of the substances that will float on a. water, b. kerosene, c, mercury.
Figure
Answer:
we can find the following.
The density of water = 7 g / 7 ml
= 1 g/ml
= 1 g/cm^{3}
The density of iron = 39.5 g / 5 cm^{3}
= 7.9 g/cm^{3}
The density of glass = 10 g / 4 cm^{3}
= 2.5 g/cm^{3}
The density of ice = 4.5 g / 5 cm^{3}
= 0.9 g/cm^{3}
The density of aluminium = 21.6 g / 8 cm^{3}
= 4.32 g/cm^{3}^{ }
The density of cork = 4 g / 10 cm^{3}
= 0.4 g/cm^{3}
The density of mercury = 40.5 g / 3 ml
= 13.5 g/ml = 13.5 g/cm^{3}
The density of kerosene = 7 g / 10 ml
= 0.7 g/ml = 0.7 g/cm^{3}
We know that if the density of a small substance is less than the density of a liquid, then it floats on the liquid. If not, it sinks in the liquid.
So, the substances that will float on water are ice and cork.
The substances that will float on kerosene are ice and cork.
The substances that will float on mercury are iron, glass, ice, aluminium and cork.
Page No 157:
Question 16:
A block of metal has a length of 20 cm, breadth 10 cm and height 5 cm. Its mass is 2.7 kg. Find the density of the metal in g/cm^{3}. Find out what the block is made of.
Answer:
Volume of the block = V = Length $\times $ Breadth $\times $ Height
Volume = V = 20 $\times $ 10 $\times $ 5
= 1000 cm^{3}
Mass of the metal block = m = 2.7 kg = 2700 gm
Density of the metal block = Mass / Volume
= 2700 / 1000
= 2.7 g/cm^{3}
Thus, the density of the metal block is 2.7 g/cm^{3}.
The metal block is made of aluminium (density = 2.7 g/cm^{3}).
Page No 157:
Question 17:
(a) Find the volume of 5 g of cork whose density is 0.25 g/cm^{3}.
(b) Find the volume of 800 g of spirit whose density is 0.25 g/cm^{3}.
Answer:
(a) Mass of the cork = 5 g
Density of the cork = 0.25 g/cm^{3}
Volume of the cork = Mass / Density
Volume of the cork = 5 / 0.25
= 20 cm^{3}^{ }
(b) Mass of the spirit = 800 g
Density of the spirit = 0.25 g/cm^{3}
Volume of the spirit = Mass / Density
Volume of the spirit = 800 / 0.25
= 3200 cm^{3}
Page No 157:
Question 18:
The density of butter is 0.9 g/cm^{3}. What is the volume of 800 g of butter?
Answer:
Density of butter = 0.9 g/cm^{3}
Mass of the butter sample = 800 g
Volume = Mass / Density
= 800 g / 0.9 g/cm^{3}
Page No 157:
Question 19:
Aluminum has a density of 2.7 g/cm^{3}. What is the mass of 200 cm^{3} of aluminum?
Answer:
Density of aluminium = 2.7 g/cm^{3}
Volume of the aluminium sample = 200 cm^{3}
Mass of the aluminium sample = Density $\times $ Volume
= 2.7 $\times $ 200
= 540 g
Page No 157:
Question 20:
A piece of steel has a volume of 12 cm^{3} and a mass of 96 g. What is its density?
Answer:
Volume of the piece of steel = 12 cm^{3}
Mass of the piece of steel = 96 g
Density of the piece of steel = Mass / Volume
= 96 g / 12 cm^{3}
= 8 g/cm^{3}
Page No 157:
Question 21:
What is the mass of 5 m^{3} of cement of density 3000 kg/m^{3}?
Answer:
Density of the cement sample = 3000 kg/m^{3}
Volume of the cement sample = 5 m^{3}
Mass of the cement sample = Density $\times $ Volume
= 3000 $\times $ 5
= 15000 kg
Page No 157:
Question 22:
What is the mass of air in a room measuring 10 m × 6 m × 5 m if the density of air is 1.3 kg/cm^{3}?
Answer:
Volume of the air in the room = Volume of the room
= 10 m × 6 m × 5 m
= 300 m^{3}
Density of the air = 1.3 kg/cm^{3}
Mass of the air = Density × Volume
= 1.3 kg/cm^{3} × 300 m^{3}^{ }
= 1.3 kg/cm^{3} × 300 × 1000000 cm^{3}^{ }
= 390000000 kg
Page No 157:
Question 23:
A lump of copper of mass 890 g is dipped into a glass filled to the brim with water. What volume of water will overflow? (The density of copper = 8.9 g/cm^{3}.)
Answer:
Mass of the lump of copper = 890 g
Density of copper = 8.9 g/cm^{3}
So, the volume of the lump of copper = Mass / Density
= 890 g / 8.9 g/cm^{3}
= 100 cm^{3}
Thus, when the lump of copper is dipped into a glass filled to the brim with water, the volume of water that will overflow is 100 cm^{3}.
Page No 157:
Question 24:
Which will occupy more space: 480 g of teak wood of density 0.48 g/cm^{3}, or 7900 g of iron of density 7.9 g/cm^{3}?
Answer:
Mass of the teak wood sample = 480 g
Density of the teak wood sample = 0.48 g/cm^{3}
Volume of the teak wood sample = Mass / Density
= 480 g / 0.48 g/cm^{3}
= 1000 cm^{3}
Mass of the iron sample = 7900 g
Density of the iron sample = 0.79 g/cm^{3}
Volume of the iron sample = Mass / Density
= 1000 cm^{3}
Both the teak wood and iron samples will occupy the same amount of space.
Page No 157:
Question 25:
The volume of 40 g of a substance is 20 cm^{3}. The density of water is 1 g/cm^{3}. Will the substance float or sink in water?
Answer:
Mass of the substance = 40 g
Volume of the substance = 20 cm^{3}
Density of the substance = Mass / Volume
= 40 g / 20 cm^{3}
As the density of the substance (2 g/cm^{3}) is higher than the density of water (1 g/cm^{3}), the substance will sink in water.
Page No 157:
Question 26:
The volume of 900 g of a substance is 1000 cm^{3}. Will the substance float or sink in water, if the density of water is 1 g/cm^{3}? What will be the mass of water displaced by this substance?
Answer:
Mass of the substance = 900 g
Volume of the substance = 1000 cm^{3}
Density of the substance = Mass / Volume
= 900 g / 1000 cm^{3}
= 0.9 g/cm^{3}
As the density of the substance (0.9 g/cm^{3}) is less than the density of the water (1 g/cm^{3}), the substance will float on water.
Mass of water displaced by the substance = Density of water × Volume of the substance
Mass of water displaced by the substance = 1 g/cm^{3}^{ }× 1000 cm^{3}^{ }
= 1000 g
Page No 157:
Question 27:
The picture shows you what happens on lowering a metal ball weighing 40 g-wt into water. Calculate the density of the metal ball.
Figure
Answer:
Weight of the metal ball in water = 40 g
Volume of the metal ball = Volume of the water displaced by it
Volume of the metal ball = 97 - 61
= 36 cm^{3}^{ }
Mass of the water displaced by it = Density of water × Volume of the metal ball
= 1 g/cm^{3} × 36 cm^{3}^{ }
= 36 g
Mass of the water displaced by the metal ball = Weight loss of the metal ball in water = 36 g
Weight of the metal ball in air = Weight of the metal ball in water + Weight loss of the metal ball in water
= 40 g + 36 g
= 76 g
Density of the metal ball = Mass of the metal ball / Volume of the ball
= 76 g / 36 cm^{3}^{ }
= 2.1 g/cm^{3}
Page No 157:
Question 28:
Akash wanted to find out the volume of a block of glass with a mass of 1 kg. He used a measuring cylinder and got an answer of 392 cm^{3}. He asked Susan to do the experiment, but she said, 'I don't have to do the experiment. I know the density of glass and can calculator the answer.' By how much did Akash's answer differ from Susan's?
Answer:
It is given that the mass of the block of glass is 1 kg. Susan knew the density of glass, so she used the formula 'Volume = Mass / Density' to find the volume of the block of glass.
Page No 157:
Question 29:
Ramesh buys six bottles of syrup, each containing 1 litre. Each empty bottle weighs 400 g. The density of the syrup 1.2 g/cm^{3}. What weight does Ramesh have to carry home?
Answer:
Mass of the syrup in each bottle = Density × Volume
= 1200 g
= 1600 g
Mass of 6 bottles with syrup = 6 × 1600
= 9600 g
= 9.6 kg
Page No 157:
Question 30:
In an experiment on density, a scientist mixed together coloured water and kerosene. The mixture was poured into a bottle and allowed to stand. Later the scientist put in a lump of ice, a small cork and an iron nail. Draw a labelled diagram showing what you see. (You will find the densities of these substances in Q15.)
Answer:
Cork floats on water and kerosene, and ice floats between the layers of kerosene and water, but an iron nail sinks in both the liquids.
Page No 157:
Question 31:
Which is more dense-seawater or river water? Why?
Answer:
Sea water is denser than river water, as it has a higher concentration of salt and minerals than river water.
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