Lakhmir Singh & Manjit Kaur: Gravitation, Solutions- 2

Page No - 123

Question 1:
Write the common unit of density.
Solution :
Grams per cubic centimtre (g/cm³).

Question 2:
What is the density of water in SI units ?
Solution :
Density of water =1000kg/m³.

Question 3:
What is the value of relative density of water ?
Solution :
Relative density of water is 1.

Question 4:
Name the quantity whose one of the units is pascal (Pa).
Solution :
Pressure has unit of Pascal (Pa).

Question 5:
State the units in which pressure is measured.
Solution :
Pressure is measured in newtons per square metre (N/m²) i.e., pascal (Pa).

Question 6:
State whether the following statements are true or false :
(a) The buoyant force depends on the nature of object immersed in the liquid
(b) Archimedes' principle can also be applied to gases.
Solution :
(a) False
(b) True

Question 7:
In which direction does the buoyant force on an object due to a liquid act ?
Solution :
Buoyant force on an object due to a liquid act s in the vertically upward direction.

Question 8:
What is the other name of buoyant force ?
Solution :
Upthrust is the other name of buoyant force.

Question 9:
Name the force which makes heavy objects appear light when immersed in a liquid.
Solution :
Buoyant force.

Question 10:
What is upthrust ?
Solution :
The upward force acting on an object immersed in a liquid is called upthrust.

Question 11:
Name the principle which gives the magnitude of buoyant force acting on an object immersed in a liquid.
Solution :
Archimedes' Principle.

Question 12:
lire relative density of mercury is 13.6. What does this statement mean ?
Solution :
The relative density of mercury is 13.6, this means that mercury is 13.6 times as heavy as an equal volume of water.

Question 13:
What name is given to 'thrust per unit area' ?
Solution :
Pressure is 'thrust per unit area'.

Question 14:
What is the ss ientific name of the 'upward force' acting on an object immersed in a liquid ?
Solution :
Buoyant force or upthrust.

Question 15:
What is meant by the term 'buoyancy' ?
Solution :
The tendency of a liquid to exert an upward force on an object placed in it, is called buoyancy.

Question 16:
What causes buoyant force (or upthrust) on a boat ?
Solution :
The buoyant force on a boat is caused by the pressure of water 'pushing up' on the bottom of the boat.

Question 17:
Why does ice float in water ?
Solution :
The density of ice is less than that of water, so ice floats in water.

Question 18:
What force acting on an area of 0.5 m² will produce a pressure of 500 Pa 
Solution :
 Force = Pressure x Area 
Force = 500 x 0.5 = 250 N  

Question 19:
An object of weight 200 N is floating in a liquid. What is the magnitude of buoyant force acting on it ?
Solution :
Since the object floats in the liquid, so the magnitude of the buoyant force exerted by the liquid is equal to the weight of the object.
Hence, buoyant force =200N

Question 20:
Name the scientist who gave he magnitude of buoyant force acting on a solid object immersed in a liquid.
Solution :
Archimedes gave the magnitude of buoyant force acting on a solid object immersed in a liquid

Question 21:
The density of gold is 19 g/cm³. Find the volume of 95 g of gold.
Solution :

Question 22:
What is the mass of 5 m³ of cement of density 3000 kg/m³ ?
Solution :
Volume=5m³
Density= 3000kg/m³ 

Question 23:
What is the density of a substance of mass 100 g and volume 10 cm³ ?
Solution :
Mass of the substance = 100g
Volume of the substance =10cm³ 

Question 24:
Why does a block of wood held under water rise to the surface when released ?
Solution :
Because the weight of the block of wood is less than the weight of an equal volume of water. So when it is completely submerged in water, the upward buoyant force on it is greater than the downward gravitational force on it. Hence, the lock rises to the surface.

Question 25:
The density of a body is 800 kg/m3. Will it sink or float when dipped in a bucket of water ? (Density' of water = 1000 kg/m³).
Solution :
The body will float when dipped in a bucket of water as its density is less than that of water.

Question 26:
Fill in the following blanks with suitable words :
(a) Force acting on a unit area is called.......................
(b) It is the................ force which makes objects appear lighter in water.
(c) A heavy ship floats in water because its......................... density is less than that of water.
(d) In fluids (liquids and gases), pressure acts in............................. directions, and pressure..................... as the depth increases.
(e) In order to sink in a fluid, the density of an object must be........................... than the..................... of the fluid.
(f) Snow shoes work by spreading out a person's........................... over a much bigger.............................
(g) If the area of a snow shoe is five times......................... than the area of an ordinary shoe, then the pressure of a snow shoe on the snow is five times........................
Solution :
(a) pressure
(b) buoyant
(c) average
(d) all; increases
(e) less; density
(f) weight; area
(g) bigger; smaller

Page No - 124

Question 27:
(a) What is the difference between the density and relative density of a substance ?
(b) If the relative density of a substance is 7.1, what will be its density in SI units ?
Solution :
(a) The density of a substance is defined as mass of the substance per unit volume. 

SI unit of density is kg/m³

The relative density of a substance is the ration of its density to that of water.

It has no unit.

Question 28:
Define thrust. What is its unit ?
Solution :
The force acting on a body perpendicular to its surface is called thrust. The SI unit of thrust is newton (N).

Question 29:
A mug full of water appears light as long as it is under water in the bucket than when it is outside water. Why ?
Solution :
A mug full of water appears light as long as it is under water because buoyant force acts on it which reduces its effective weight and makes it appear lighter.

Question 30:
What happens to the buoyant force as more and more volume of a solid object is immersed in a liquid ? When does the buoyant force become maximum ?
Solution :
As more and more volume of the solid object is immersed in the liquid, the upward 'buoyant force' also keeps on increasing. When the object is completely immersed in the liquid, the buoyant force acting on the solid becomes maximum and remains constant thereafter.

Question 31:
Why do we feel light on our feet when standing in a swimming pool with water up to our armpits ?
Solution :
As more and more volume of our body is immersed in water, the apparent weight of the body goes on decreasing and the body seems to become lighter. This is due to the increase in upward buoyant force acting on the body.

Question 32:
Explain why, big boulders can be moved easily by flood.
Solution :
Big boulders weig much less while in water and as such are easily moved by the flood.

Question 33:
An iron nail sinks in water but it floats in mercury. Why ?
Solution :
An iron nail sinks in water but it floats in mercury because density of iron is more than that of water but less than that of mercury.

Question 34:
Explain why, a piece of glass sinks in water but it floats in mercury.
Solution :
A piece of glass sinks in water but it floats in mercury because density of glass is more than that of water but less than that of mercury.

Question 35:
Steel sinks in water but a steel boat floats. Why ?
Solution :
A piece of steel sinks in water because steel is denser than water. However, a steel ship is a hollow object made of steel and contains a lot of air in it. Due to presence of a lot of air in it, the average density of the ship becomes less than the density of water. Hence a ship floats in water.

Question 36:
Explain why, school bags are provided with wide straps to carry them.
Solution :
School bags have wide straps so that their weight may spread over a large area of shoulder producing less pressure on the shoulder.

Question 37:
Why does a sharp knife cut objects more effectively than a blunt knife ?
Solution :
A sharp knife cuts objects easily because due to its very thin edge, the force of our hand falls on a very small area of the object producing large pressure.

Question 38:
Explain why, wooden (or concrete) sleepers are kept below the railway line.
Solution :
Concrete or wooden
sleepers are kept below the railway line so that the weight of passing train
is spread over a large area of ground and the track may not sink into the
ground.

Question 39:
Explain why, a wide steel belt is provided over the wheels of an army tank.

The density of iron or steel is much higher than that of water, so an object made of iron or steel (like this car) sinks in water.
Solution :
A wide steel belt is provided over the wheels of an army tank so that they exert less pressure on the ground and do not sink into it.

Question 40:
Explain why, the tip of a sewing needle is sharp.

Solution :
The tip of the sewing needle is sharp so that due to its sharp tip, the needle may put the force on a very small area of the cloth, producing a large pressure sufficient to pierce the cloth being stitched.

Question 41:
When is the pressure on the ground more-when a man is walking or when a man is standing ? Explain.
Solution :
When a man is walking, then at one time only one foot is on the ground. Due to this, the force of weight of man falls on a smaller area of the ground and produces more pressure on the ground. On the other hand, when the man is standing, then both his feet are on the ground. Due to this, the weight of the man falls on a larger area of the ground and produces lesser pressure on the ground.

Question 42:
Explain why, snow shoes stop you from sinking into soft snow.
Solution :
Snow shoes stop us from sinking into soft snow because due to large area of snow shoes, our weight is spread over a large area of the snow producing small pressure.

Question 43:
Explain why, when a person stands on a cushion, the depression is much more than when he lies down on it.
Solution :
When a person stands on a cushion then only his two feet (having small area) are in contact with the cushion. Due to this the weight of man falls on a small area of the cushion producing a large pressure causing a big depression in the cushion. On the other hand, when the same person lies down on the cushion, then his whole body (having large area) is in contact with the cushion. Here, his weight falls on a much larger area of the cushion producing much smaller pressure and very little depression in the cushion.

Question 44:
Use your ideas about pressure to explain why it is easier to walk on soft sand if you have flat shoes rather than shoes with sharp heels.
Solution :
Flat shoes have greater area in contact with the soft sand as compared to heels. Due to this, there is less pressure on soft sand because of which they do not sink much in the sand and it is easy to walk on it.

Question 45:
Explain why, a nail has a pointed tip.

A nail has a pointed tip

Solution :
A nail has a pointed tip, so that when it is hammered, the force of hammer is transferred to a very small area of wood creating a large pressure which pushes the nail into the wood.

Page No -125

Question 46:
Explain why, buildings and dams have wide foundations.
Solution :
The foundations of buildings and dams are laid on a large area of ground so that the weight of the building or dam produces less pressure on the ground and they may not sink into the ground.

Question 47:
Why does a ship made of iron and steel float in water whereas a small piece of iron sinks in it ?

The density of iron or steel is much higher than that of water, so an object made of iron or steel (like this car) sinks in water.

Solution :
A ship made of iron and steel is a hollow object which contains a lot of air in it. Due to the presence of a lot of air in it, the average density of the ship becomes less than the density of water. Hence a ship floats in water.
On the other hand, a piece of iron is denser than water, so it sinks in water.

Question 48:
Why do camels have large flat feet ?

Solution :
Camels have large flat feet so that there is a greater area in contact with the sand which produces less pressure on the sand and the camels can move easily on the sand.

Question 49:
Name these forces :
(a) the upward push of water on a submerged object
(b) the force which wears away two surfaces as they move over one another
(c) the force which pulled the apple off Isaac Newton's tree.
(d) the force which stops you falling through the floor.
Solution :
(a) Buoyant force
(b) Force of friction
(c) Gravitational force
(d) Reaction force

Question 50:
A pressure of 10 Pa acts on an area of 3.0 m². What is the force acting on the area ? What force will be exerted by the application of same pressure if the area is made one-third ?
Solution :
If the area is made one-third i.e. 1m², then the force would be:

If the area is made one-third i.e. 1m², then the force would be:

Question 51:
A girl is wearing a pair of flat shoes. She weighs 550 N. The area of contact of one shoe with the ground is 160 cm². What pressure will be exerted by the girl on the ground :
(a) if she stands on two feet ?
(b) if she stands on one foot ?
Solution :
Force, F= 550N
Area of contact of one shoe =160 cm² =160 x 10^-4m²
Area of contact with two shoes =160 x 2 =320 cm²=320 x 10^-4m² 

Question 52:
Calculate the density of an object of volume 3 m³ and mass 9 kg. State whether this object will float or sink in water. Give reason for your answer.
Solution : 

volume = 3 m³

Mass = 9Kg

and density of water = 1000kg/m³ 
The object will float in the water as the density of the object is less than the density of water. 

Question 53:
An object weighs 500 grams in air. This object is then fully immersed in water. State whether it will weigh less in water or more in water. Give reason for your answer.
Solution :
The object will weigh less in water because an upward force (buoyant force) equal to the weight of water displaced acts on the object when immersed in water which reduces its weight apparently.

Question 54:
(a) Write down an equation that defines density.
(b) 5 kg of material A occupy 20 cm³ whereas 20 kg of materia! B occupy 90 cm³. Which has the greater density : A or B ? Support your answer with calculations.

Solution :

For material B:
Mass =20kg
Volume =90 cm³ = 90x 10^-6m³

Density of material A is more than density of material B.

Question 55:
(a) Define buoyant force. Name two factors on which buoyant force depends.
(b) What is the cause of buoyant force ?
(c) When a boat is partially immersed in water, it displaces 600 kg of water. How much is the buoyant force acting on the boat in newtons ? (g = 10 m s^-2)
Solution :
(a) The upward force acting on an object immersed in a liquid is called buoyant force.
Factors affecting buoyant force:
(i) Volume of object immersed in the liquid,
(ii) Density of the liquid.
(b) The cause of buoyant force is the greater upward pressure exerted by water underneath the object..
(c) Mass of water displaced = 600kg
Weight of water displaced, W =m x g
=600 x 10 =6000N
Since, the weight of water displaced by the boat is 6000N, therefore the buoyant force acting on the boat will also be 6000N.

Question 56:
(a) State the principle of flotation.
(b) A floating boat displaces water weighing 6000 newtons.
(i) What is the buoyant force on the boat ?
(ii) What is the weight of the boat ?
Solution :
(a) According to the principle of floatation: An object will float in a liquid if the weight of object is equal to the weight of liquid displaced by it.
Weight of object = Weight of liquid displaced by it.
(b) Weight of water displaced by boat= 6000N
(i) Buoyant force =6000N, as the weight of water displaced is equal to buoyant force.
(ii) Weight of a floating object = Weight of water displaced by it = 6000N

Question 58:
(a) Define pressure.
(b) What is the relation between pressure, force and area ? ,
(c) Calculate the pressure when a force of 200 N is exerted on an area of:
(i) 10 m²
(ii) 5 m²
Solution :
(a) Pressure is the force acting perpendicularly on a unit area of the object.

Page No -126

Question 59:
(a) What are fluids ? Name two common fluids.
(b) State Archimedes' principle.
(c) When does an object float or sink when placed on the surface of a liquid ?
Solution :
(a) Those substances which can flow easily are called fluids. All the liquid and gases are fluids, like water, air etc.
(b) Archimedes' Principle :
When an object is wholly (or partially) immersed in a liquid, it experiences a buoyant force (or upthrust) which is equal to the weight of liquid displaced by the object.
Buoyant force on an object = weight of liquid displaced by that object
(c) If the buoyant force exerted by the liquid is less than the weight of the object, the object will sink in the liquid. If the buoyant force exerted by the liquid is equal to or greater than the weight of the object, the object will float in the liquid.

Question 60:
(a) How does a boat float in water ?
(b) A piece of steel has a volume of 12 cm³, and a mass of 96 g. What is its density :
(i) in g/cm³ ?
(ii) in kg/m³ ?
Solution :
(a) A floating boat displaces water equal to its own weight. This displaced water exerts buoyant force to balance the weight of boat and keep it afloat.
(b) (i) Mass = 96 g
Volume = 12cm³

Question 61:
An elephant weighing 40,000 N stands on one foot of area 1000 cm² whereas a girl weighing 400 N is standing on one 'stiletto' heel of area 1 cm². 

(a) Which of the two, elephant or girl, exerts a larger force on the ground and by how much ?
(b) What pressure is exerted on the ground by the elephant standing on one foot ?
(c) What pressure is exerted on the ground by the girl standing on one heel ?
(d) Which of the two exerts larger pressure on the ground : elephant or girl ?
(e) What is the ratio of pressure exerted by the girl to the pressure exerted by the elephant ?
Solution :
Weight of elephant=40000N
Area of one foot =1000 cm²= 1000 x 10^-4m²
Weight of girl=400N
Area of heel of girl =1 cm²=1 x 10^-4m²
(a) Elephant has a larger weight of 40000N, therefore, elephant exerts a larger force on the ground. Elephant exerts a larger force on the ground by 40000N - 400 N=39600N.
(b)Weight of elephant = 40000N
Area of one foot =1000cm²= 1000 x 10^-4m² 

The pressure exerted by girl is 10 times greater than the exerted by the elephant.

Page No -127

Question 72:
If two equal weights of unequal volumes are balanced in air, what will happen when they are completely dipped in water ? Why ?
Solution :
The two equal weights of unequal volumes which are balanced in air, will get imbalanced when they are completely dipped in water because due to their unequal volumes, they will displace unequal volumes of water and hence suffer unequal loss in weight.

Question 73:
Two different bodies are completely immersed in water and undergo the same loss in weight. Is it necessary that their weights in air should also be the same ? Explain.
Solution :
No, it is not necessary that their weights in air should also be the same. This is because the two bodies have undergone the same loss in weight on completely immersing in water due to their equal volumes and not because of their equal weights, so they may have different weights in air.

Question 74:
A body floats in kerosene of density 0.8 x 10³ kg/m³ up to a certain mark. If the same body is placed in water of density 1.0 x 10³ kg/m³, will it sink more or less ? Give reason for your answer.
Solution :
The body will sink less in water. This is because the density of water is more than that of kerosene due to which water will exert a greater upward buoyant force on the body.

Question 75:
Giving reasons state the reading on a spring balance when it is attached to a floating block of wood which weighs 50 g in air.
Solution :
The reading on spring balance will be zero. This is because the weight of floating block of wood is fully supported by the liquid in which it is floating and hence it does not exert any force on the spring balance.

Question 76:
If a fresh egg is put into a beaker filled with water, it sinks. On dissolving a lot of salt in the water, the egg begins to rise and then floats. Why ?
Solution :
When a lot of salt is dissolved in water, then the density of salt solution becomes much more than pure water. Due to its much higher density, the salt solution exerts a greater upward buoyant force on the egg making it rise and then float.

Page No:128

Question 77:
A beaker full of water is suspended from a spring balance. Will the reading of the balance change :
(a) if a cork is placed in water ?
(b) if a piece of heavy metal is placed in it ?
Give reasons for your answer.
Solution :
The reading of spring balance will not change if a cork is placed in water because cork, being lighter than water, floats in water.
(b)The reading of spring balance will change if a piece of heavy metal is placed in
water because heavy metal being denser than water, sinks in water.

Question 78:
When a golf ball is lowered into a measuring cylinder containing water, the water level rises by 30 cm³ when the ball is completely submerged. If the mass of ball in air is 33 g, find its density.
Solution :
Volume of golf ball = rise in water level = 30 cm³

Question 79: A boy gets into a floating boat.

• What happens to the boat ?
• What happens to the weight of water displaced ?
• What happens to the buoyant force on the boat ?

Solution :
a) The boat sinks a little more in water, that is, the boat floats lower in water.
b) The weight of water displaced (by the submerged part of the boat) increases.
c) The buoyant force acting on the boat increases.

Question 80:
A y kg sheet of tin sinks in water but if the same sheet is converted into a box or boat, it floats. Why ?
Solution :
The sheet of tin sinks in water because the density of tin is higher than that of water. When the same sheet of tin is converted into a box or a boat, then due to the trapping of lot of 'light' air in the box or boat, the average density of the box or boat made of tin sheet becomes lower than that of water and hence it floats in water.