LAKHMIR SINGH AND MANJIT KAUR Solutions for Class 9 Physics Chapter 3 - Gravitation
Chapter 3 - Gravitation Exercise 100
What is the value of gravitational constant G (i) on the earth, and (ii) on the moon?
Value of gravitational constant G on the earth and the moon is = 6.67 x 10^{-11}Nm^{2}/kg^{2}
Note that the value of G always remains constant irrespective of the location.
Which force is responsible for the moon revolving round the earth?
Gravitational force is responsible for the moon revolving round the earth.
Does the acceleration produced in a freely falling body depend on the mass of the body?
No, the acceleration produced in a freely falling body is independent of the mass of the body.
Name the scientist who gave the three laws of planetary motion.
Johannes Kepler gave the three laws of planetary motion.
Name the scientist who explained the motion of planets on the basis of gravitational force between the sun and planets.
Newton explained the motion of planets on the basis of gravitational force between the sun and planets.
State the Kepler's Law which is represented by the relation _{.}
Kepler's law of periods states that: The cube of the mean distance of a planet from the sun is directly proportional to the square of time it takes to move around the sun.
Which of the Kepler's law of planetary motion led Newton to establish the inverse-square rule for gravitational force between two bodies?
Kepler's third law of planetary motion led Newton to establish the inverse-square rule for gravitational force between two bodies.
Name the property of earth which is responsible for extremely small acceleration being produced in it as a result of attraction by other small objects..
Extremely large mass of the earth.
What is the acceleration produced in a freely falling body of mass 10kg? (Neglect air resistance)
Acceleration produced in a freely falling body, irrespective of its mass, is 9.8m/s^{2}
When an object is dropped from a height, it accelerates and falls down. Name the force which accelerates the object.
Gravitational force of the earth.
Give the formula for the gravitational force F between two bodies of masses M and m kept at a distance d from each other.
The gravitational force F between two bodies of masses M and m kept at a distance d from each other is :
_{}
Here, Gravitational constant, G=6.7 x10^{-11}Nm^{2} kg^{-2}
What force is responsible for the earth revolving round the sun?
Gravitational force is responsible for the earth revolving round the sun.
What name has been given to the force with which two objects lying apart attract each other?
Gravitational force causes two objects lying apart attract each other.
What type of force is involved in the formation of tides in the sea?
Gravitational force (exerted mainly by the moon and to some extent by the sun) is involved in the formation of tides in the sea.
Which force is responsible for holding the solar system together?
Gravitational force of the sun holds the solar system together.
What is the weight of a 1kilogram mass on the earth? (g=9.8m/s^{2})
Weight, W = m x g
= 1 kg x 9.8m/s^{2}=9.8 N
On what factor/factors does the weight of a body depend?
The weight of a body is directly proportional to its mass.
It also depends on the acceleration due to gravity which varies from place to place.
As the altitude of a body increases, do the weight and mass both vary?
Weight of the body varies with altitude; mass of an object is constant.
If the same body is taken to places having different gravitational field strength, then what will vary: its weight or mass?
Its weight varies; mass of an object is constant.
If the mass of an object be 10kg, what is its weight? (g=9.8m/s^{2})
Weight, W=m x g
= 10 x 9.8 =98 N
The weight of a body is 50N. What is its mass? (g=9.8m/s^{2})
Weight, W=m x g
_{}
A body has a weight of 10kg on the surface of earth. What will be its weight when taken to the centre of the earth?
Its weight will be zero as value of g is zero at the centre of the earth.
Write down the weight of a 50 kg mass on the earth. (g=9.8m/s^{2})
Weight, W=m x g
=50 x 9.8=490N
If the weight of a body on the earth is 6N, what will it be on the moon?
Weight of the body on the surface of moon will be 1N approx. as the value of g on the surface of moon is one-sixth that of the earth.
State whether the following statements are true or false:
(a) A falling stone also attracts the earth.
(b) The force of gravitation between two objects depends on the nature of medium between them.
(c) The value of G on the moon is about one-sixth of the value of G on the earth.
(d) The acceleration due to gravity acting on a freely falling body is directly proportional to the mass of the body.
(e) The weight of an object on the earth is about one-sixth of the weight on the moon.
(a) True
(b) False
(c) False
(d) False
(e) False
Chapter 3 - Gravitation Exercise 101
Fill in the blanks with suitable words:
(a) The acceleration due to gravity on the moon is about______ of that on the earth.
(b) In order that the force of gravitation between two bodies may become noticeable and cause motion, one of the bodies must have an extremely large _______.
(c) The weight of an object on the earth is about _____of its weight on the moon.
(d) The weight of an object on the moon is about ______of its weight on the earth.
(e) The value of g on the earth is about _____ of that on the moon.
(f) If the weight of a body is 6N on the moon, it will be about _____ on the earth.
(a) One-sixth
(b) Mass
(c) Six times
(d) One-sixth
(e) Six times
(f) 36N
Explain what is meant by the equation:
_{}
Where the symbols have their usual meanings.
This is the acceleration produced by the earth. It is also called acceleration due to gravity.
_{ }
_{where, G= gravitational constant}
_{ M= mass of the earth.}
_{ R=radius of the earth}
(a)What do you mean by the term 'free fall'?
(b)During a free fall, will heavier objects accelerate more than the lighter ones?
(a)The falling of a body from a height towards the Earth under the gravitational force of the Earth (with no other forces acting on it) is called free fall.
(b)No, acceleration is independent of the mass of the body during free fall.
Can we apply Newton's third law to the gravitational force? Explain your answer.
Yes, Newton's third law of motion holds good for the force of gravitation. This means that when earth exerts a force of attraction on an object, then the object also exerts an equal force on the earth, in the opposite direction.
Give reason for the following:
The force of gravitation between two cricket balls is extremely small but that between a cricket ball and the earth is extremely large.
The force of gravitation between two bodies is directly proportional to the product of their masses.
_{}
Since the mass of cricket balls is very small as compared to that of the earth, so the force of gravitation between two cricket balls is extremely small while that between a ball and the earth is extremely large.
Describe how the gravitational force between two objects depends on the distance between them.
The gravitational force F between two bodies of masses M and m kept at a distance d from each other is :
_{}
The force between two bodies is inversely proportional to the square of the distance between them. That is,
Therefore , if we double the distance between two bodies, the gravitational force becomes one-fourth and if we halve the distance between two bodies, then the gravitational force becomes four times_{.}
What happens to the gravitational force between two objects when the distance between them is:
(i) Doubled?
(ii) Halved?
(a) If we double the distance between two bodies, the gravitational force becomes one-fourth.
(b) If we halve the distance between two bodies, then the gravitational force becomes four times.
State two applications of universal law of gravitation.
(i) Universal law of gravitation is used to determine the masses of the sun, the earth and the moon accurately.
(ii) Universal law of gravitation helps in discovering new stars and planets.
Explain why, if a stone held in our hand is released, it falls towards the earth.
This is because the earth exerts a force of attraction (called gravity) on the stone and pulls it down.
Calculate the force of gravitation between two objects of masses 50kg and 120kg respectively kept at a distance of 10 m from one another.(gravitational constant, G=6.7 x 10^{-11} Nm^{2}/kg^{2})
m=50kg
M=120kg
Distance, d=10m
G=6.7 x 10^{-11} Nm^{2}/kg^{2}
What is the force of gravity on a body of mass 150 kg lying on the surface of the earth? (mass of earth = 6 x 10^{24}kg; Radius of earth= 6.4 x 10^{6}m; G=6.7 x 10^{-11} Nm^{2}/kg^{2})
Force due to gravity,
The mass of sun is 2 x10^{30}kg and the mass of earth is 6 x 10^{24}kg. If the average distance between the sun and the earth be 1.5 x 10^{8}km, calculate the force of gravitation between them.
Distance d=1.5 x 10^{8 }km= 1.5 x 10^{11 }m
Mass of the sun, m=2 x10^{30 }kg
Mass of the earth, M= 6 x 10^{24}kg
Force of gravitation, _{}
_{}
A piece of stone is thrown vertically upwards. It reaches the maximum height in 3 seconds. If the acceleration of the stone be 9.8 m/s^{2} directed towards the ground, calculate the initial velocity of the stone with which it is thrown upwards.
Initial velocity of the stone, u=?
Final velocity of stone, v=0
Acceleration due to gravity, g= -9.8m/s^{2}
Time, t=3 sec
Using relation, v=u + gt
0 = u -9.8 x 3
u =29.4m/s
A stone falls from a building and reaches the ground 2.5 seconds later. How high is the building? (g=9.8m/s^{2})
Initial velocity, u=0m/s
Acceleration due to gravity, g=9.8m/s^{2}
Time taken to reach the ground, t=2.5 sec
Height, h=?
Using relation,
_{ }
A stone is dropped from a height of 20 m.
(i) How long will it take to reach the ground?
(ii) What will be its speed when it hits the ground? (g=10m/s^{2})
Height, s=20m
Initial velocity, u=0
Acceleration due to gravity, g=10m/s^{2}
Final velocity, v=?
Time taken, t=?
(i) Using relation,
(ii) For a freely falling body:
v^{2} = u^{2} + 2gh
= (0)^{2} + 2 x (10) x (20)
So, v^{2} =400
The speed of stone when it hits the ground will be 20m/s.
A stone is thrown vertically upwards with a speed of 20m/s. How high will it go before it begins to fall? (g=9.8m/s^{2})
Initial velocity, u=20m/s
Final velocity, v=0
Acceleration due to gravity, g=-9.8m/s^{2}
Height, h=?
Using relation, for a freely falling body:
v^{2} = u^{2} + 2gh
(0)^{2} = (20)^{2} + 2 x (-9.8) x h
0-400 = -19.6 h
h= 400/19.6 = 20.4 m
When a cricket ball is thrown vertically upwards, it reaches a maximum height of 5 metres.
(a) What was the initial speed of the ball?
(b) How much time is taken by the ball to reach the highest point? (g=10m/s^{2})
Initial velocity, u=?
Final velocity, v=0
Acceleration due to gravity, g=-10m/s^{2}
Height, h=5 m
(a) For a freely falling body:
v^{2} = u^{2} + 2gh
(0)^{2} = u^{2}+ 2 x(-10)x 5
0= u^{2} -100
u^{2}= 100
So, u=10m/s
(b) Using relation, v=u + gt
0 = 10 + (-10) t
-10= -10 t
t=1sec
Write the differences between mass and weight of an object.
Mass |
Weight |
1. The mass of an object is the quantity of matter contained in it. |
1. The weight of an object is the force with which it is attracted towards the centre of the earth. |
2. SI unit of mass is kilogram (kg). |
2. SI unit of mass is newton (N). |
3. The mass of an object is constant. |
3. The weight of an object is not constant. It changes with the change in acceleration due to gravity. |
4. The mass of an object can never be zero. |
4. The weight of an object can be zero. |
Can a body have mass but no weight? Give reasons for your answer.
Yes, weight of a body is not constant, it varies with the value of acceleration due to gravity, g.
Weight of a body is zero, when it is taken to the centre of the earth or in the interplanetary space, where g=0.
Chapter 3 - Gravitation Exercise 102
A force of 20N acts upon a body whose weight is 9.8N. What is the mass of the body and how much is its acceleration? (g=9.8m/s^{2})
Weight= 9.8N
W= m x g
9.8 =m x 9.8
m= 1kg
Force, F= mass x acceleration
20 N = 1kg x a
Acceleration, a=20m/s^{2}
A stone resting on the ground has a gravitational force of 20 N acting on it. What is the weight of the stone? What is its mass? (g=10m/s^{2}).
Weight, W= m x g
20=m x 10
m=2 kg
An object has mass of 20kg on earth. What will be its (i) mass, and (ii) weight, on the moon? (g on moon=1.6 m/s^{2})
(i) Its mass will be 20 kg as mass is a constant quantity.
(ii) Weight, W= m x g
=20 x 1.6=32 N
Which is more fundamental, the mass of a body or its weight? Why?
The mass of a body is more fundamental because mass of a body is constant and does not change from place to place.
How much is the weight of an object on the moon as compared to its weight on the earth? Give reason for your answer.
The weight of an object on the moon is about one-sixth of its weight on the earth. This is because the value of acceleration due to gravity on the moon is about one-sixth of that on the earth.
(a) Define mass of a body. What is the SI unit of mass?
(b) Define weight of a body. What is the SI unit of weight?
(c) What is the relation between mass and weight of a body?
(a) The mass of a body is the quantity of matter contained in it. The SI unit of mass is kilogram (kg).
(b) The weight of a body is the force with which it is attracted towards the centre of the earth. The SI unit of weight is newton (N).
(c) Weight, W =m x g, i.e. the weight of a body is directly proportional to its mass.
(a) State the universal law of gravitation. Name the scientist who gave this law.
(b) Define gravitational constant. What are the units of gravitational constant?
(a) According to universal law of gravitation: Every body in the universe attracts every other body with a force (F) which is directly proportional to the product of their masses (m and M) and inversely proportional to the square of the distance (d) between them.
Sir Isaac Newton gave this law.
(b) The gravitational constant G is numerically equal to the force of gravitation which exists between two bodies of unit masses kept at a unit distance from each other.
Units of gravitational constant= Nm^{2}/kg^{2}
(a) What do you understand by the term 'acceleration due to gravity of earth'?
(b) What is the usual value of acceleration due to gravity of earth?
(c) State the SI unit of acceleration due to gravity.
(a) The uniform acceleration produced in a freely falling body due to the gravitational force of the earth is called acceleration due to gravity of earth.
(b) Usual value of acceleration due to gravity, g=9.8 m/s^{2}.
(c) SI unit of acceleration due to gravity is m/s^{2}.
(a) Is the acceleration due to gravity of earth 'g' a constant? Discuss.
(b) Calculate the acceleration due to gravity on the surface of a satellite having a mass of 7.4 x 10^{22}kg and a radius of 1.74 x 10^{6}m (G= 6.7 x 10^{-11 }Nm^{2}/kg^{2}). Which satellite do you think it could be?
(a) No, the value of acceleration due to gravity (g) is not constant at all the places on the surface of the earth. Since the radius of the earth is minimum at the poles and maximum at the equator, the value of g is maximum at the poles and minimum at the equator. As we go up from the surface of the earth, the distance from the centre of the earth increases and hence the value of g decreases. The value of g also decreases as we go down inside the earth.
(b) Acceleration due to gravity,
Mass, M= 7.4 x 10^{22}kg
Radius, R =1.74 x 10^{6}m
Gravitational constant, G= 6.7 x 10^{-11}Nm^{2}/kg^{2}
^{ }
As the value of g =1.637m/s^{2}, which is one sixth the value of g on earth, the satellite could be moon.
State and explain Kepler's laws of planetary motion. Draw diagrams to illustrate these laws.
Kepler's first law: The planets move in elliptical orbits around the sun, with the sun at one of the two foci of the elliptical orbit. This law means that the orbit of a planet around the sun is an ellipse and not an exact circle. An elliptical path has two foci, and the sun is at one of the two foci of the elliptical path.
Kepler's Second law states that: Each planet revolves around the sun in such a way that the line joining the planet to the sun sweeps over equal areas in equal intervals of time. This means that a planet does not move with constant speed around the sun. The speed is greater when the planet is nearer the sun, and less when the planet is farther away from the sun.
Kepler's Third Law states that: The cube of the mean distance of a planet from the sun is directly proportional to the square of time it takes to move around the sun.
_{}
^{ }
The mass of a planet is 6 x 10^{24} kg and its diameter is 12.8 x10^{3 }km. If the value of gravitational constant be 6.7 x 10^{-11} Nm^{2}/kg^{2}, calculate the value of acceleration due to gravity on the surface of the planet. What planet could this be?
Acceleration due to gravity,
_{}
Mass, M = 6x 10^{24}kg
Diameter = 12.8 x 10^{3} km = 12.8 x 10^{6} m
Radius, R = (12.8 x 10^{6})/2 =6.4x 10^{6}m
Gravitational constant, G= 6.7 x 10-11Nm^{2}/kg^{2}_{ }
_{ }_{ }
As the value of g=9.8m/s^{2}, the planet could be Earth.
Chapter 3 - Gravitation Exercise 103
If the distance between two masses is increased by a factor of 5, by what factor would the mass of one of them have to be altered to maintain the same gravitational force? Would this be an increase or decrease in the mass?
Gravitational force is given by:
_{}
Distance between two masses is increased s.t. new distance is D= 5 d
New gravitational force F_{1} = F
Let on of the mass is changed to m_{1} so as to maintain the same gravitational force.
_{ }
m_{1} = 25m
Hence one of the masses should be increased by 25 times in order to have the same gravitational force.
Universal law of gravitation states that every object exerts a gravitational force of attraction on every other object. If this is true, why don't we notice such forces? Why don't the two objects in a room move towards each other due to this force?
In order to be able to notice the gravitational force of attraction between any two objects, at least one of the objects on the earth should have an extremely large mass. Since no object on the earth have an extremely large mass, we cannot notice such forces.
The two objects in a room do not move towards each other because due to their small masses, the gravitational force of attraction between them is very, very weak.
Suppose a planet exists whose mass and radius both are half those of the earth. Calculate the acceleration due to gravity on the surface of this planet.
Acceleration due to gravity of earth,
_{}_{ }
If mass of planet, m= M/2
And radius of planet, r= R/2
Acceleration due to gravity on the surface of planet will be:
_{}
Chapter 3 - Gravitation Exercise 104
A coin and a piece of paper are dropped simultaneously from the same height. Which of the two will touch the ground first? What will happen if the coin and the piece of paper are dropped in vacuum? Give reason for your answer.
The coin reaches the ground first as compared to the piece of paper because it experiences lesser resistance from air than that felt by paper.
If the coin and the piece of paper are dropped in vacuum, both of them will touch the ground at the same time.
A stone and the earth attract each other with an equal and opposite force. Why then we see only the stone falling towards the earth but not the earth rising towards the stone?
The mass of a stone is very small, due to which the gravitational force produces a large acceleration in it. Due to large acceleration of stone, we see stone falling towards the earth. The mass of earth is, however, very, very large. Due to the very large mass of the earth, the same gravitational force produces very, very small acceleration in the earth, that it cannot be observed. And hence we do not see the earth rising up towards the stone.
What is the actual shape of the orbit of a planet around the sun? What assumption was made by Newton regarding the shape of an orbit of a planet around the sun for deriving his inverse square rule from Kepler's third law of planetary motion?
The actual shape of the orbit of a planet around the sun is elliptical.
The assumption made by the Newton regarding the shape of an orbit of a planet around the sun was that the orbit of a planet around the sun is 'circular'.
The values of g at six distances A, B, C, D, E and F from the surface of the earth are found to be 3.08m/s^{2},9.23m/s^{2} ,0.57 m/s^{2}, 7.34 m/s^{2} , 0.30 m/s^{2} , and 1.49 m/s^{2} , respectively.
(a) Arrange these values of g according to the increasing distances from the surface of the earth (keeping the value of g nearest to the surface of the earth first)
(b) If the value of distance F be 10000km from the surface of the earth, state whether this distance is deep inside the earth or high up in the sky? Give reason for your answer.
(a) 9.23 m/s^{2} , 7.34 m/s^{2} , 3.08 m/s^{2} , 1.49 m/s^{2} , 0.57 m/s^{2} , 0.30 m/s^{2}
(b) This distance F of 10000 km is high up in the sky. The distance of 10000 km cannot be deep inside the earth because the radius of earth is only about 6400km and the value of g at the centre of earth becomes zero.
Chapter 3 - Gravitation Exercise 123
Write the common unit of density.
Grams per cubic centimtre (g/cm^{3}).
What is the density of water in SI units?
Density of water =1000kg/m^{3}.
What is the value of relative density of water?
Relative density of water is 1.
Name the quantity whose one of the units is Pascal (Pa).
Pressure has unit of Pascal (Pa).
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.
(a) False
(b) True
In which direction does the buoyant force on an object due to a liquid act?
Buoyant force on an object due to a liquid acts in the vertically upward direction.
What is the other name of buoyant force?
Upthrust is the other name of buoyant force.
Name the force which makes heavy objects appear light when immersed in a liquid.
Buoyant force.
What is upthrust?
The upward force acting on an object immersed in a liquid is called upthrust.
Name the principle which gives the magnitude of buoyant force acting on an object immersed in a liquid.
Archimedes' Principle.
The relative density of mercury is 13.6. What does this statement mean?
The relative density of mercury is 13.6, this means that mercury is 13.6 times as heavy as an equal volume of water.
What name is given to 'thrust per unit area'?
Pressure is 'thrust per unit area'.
What is the scientific name of the 'upward force' acting on a object immersed in a liquid?
Buoyant force or upthrust.
What is meant by the term 'Buoyancy'?
The tendency of a liquid to exert an upward force on an object placed in it, is called buoyancy.
What causes buoyant force (or upthrust) on a boat?
The buoyant force on a boat is caused by the pressure of water 'pushing up' on the bottom of the boat.
Why does ice float in water?
The density of ice is less than that of water, so ice floats in water.
What force acting on an area of 0.5 m^{2} will produce a pressure of 500 Pa?
_{}
An object of weight 200N is floating in a liquid. What is the magnitude of buoyant force acting on it?
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
Name the scientist who gave the magnitude of buoyant force acting on a solid object immersed in a liquid.
Archimedes gave the magnitude of buoyant force acting on a solid object immersed in a liquid
The density of gold is 19g/cm^{3}. Find the volume of 95 g of gold.
_{}
What is the mass of 5m^{3} of cement of density 3000kg/m^{3}?
Volume=5m^{3}
Density= 3000kg/m^{3}
_{ }
What is the density of a substance of mass 100g and volume 10 cm^{3}?
Mass of the substance = 100g
Volume of the substance =10cm^{3}
_{}
Why does a block of wood held under water rise to the surface when released?
The density of a body is 800kg/m^{3}. Will it sink or float when dipped in a bucket of water? (Density of water=1000kg/m^{3}).
The body will float when dipped in a bucket of water as its density is less than that of water.
Fill in the blanks:
(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 or 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 _____.
(a) pressure
(b) buoyant
(c) average
(d) all; increases
(e) less; density
(f) weight; area
(g) bigger; smaller
Chapter 3 - Gravitation Exercise 124
(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?
(a) The density of a substance is defined as mass of the substance per unit volume.
SI unit of density is kg/m^{3}.
The relative density of a substance is the ratio of its density to that of water.
It has no units.
(b)
Define thrust. What is its unit?
The force acting on a body perpendicular to its surface is called thrust.
The SI unit of thrust is newton (N).
A mug full of water appears light as long as it is under water in the bucket than when it is outside water. Why?
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.
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?
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.
Why do we feel light on our feet when standing in a swimming pool with water up to our armpits?
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.
Explain why, big boulders can be moved easily by flood.
Big boulders weig much less while in water and as such are easily moved by the flood.
An iron nail sinks in water but it floats in mercury. Why?
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.
Explain why, a piece of glass sinks in water but it floats in mercury.
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.
Steel pin sinks in water but a steel boat floats. Why?
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.
Explain why, school bags are provided with wide straps to carry them.
School bags have wide straps so that their weight may spread over a large area of shoulder producing less pressure on the shoulder.
Why does a sharp knife cut objects more effectively than a blunt knife?
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.
Explain why, wooden (or concrete) sleepers are kept below the railway line.
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.
Explain why, a wide steel belt is provided over the wheels of an army tank.
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.
Explain why, the tip of the sewing needle is sharp.
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.
When is the pressure on the ground more- when a man is walking or when a man is standing? Explain
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.
Explain why, snow shoes stop you from sinking into soft snow.
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.
Explain why, when a person stands on a cushion, the depression is much more than when he lies down on it.
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.
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.
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.
Explain why, a nail has a pointed tip.
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.
Chapter 3 - Gravitation Exercise 125
Explain why, buildings and dams have wide foundations.
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.
Why does a ship made of iron and steel float in water whereas a small piece of iron sinks in it?
On the other hand, a piece of iron is denser than water, so it sinks in water.
Why do camels have large feet?
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.
Name these forces:
(a) The upward push of water on the 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.
(a) Buoyant force
(b) Force of friction
(c) Gravitational force
(d) Reaction force
A pressure of 10 Pa acts on an area of 3.0m^{2}. 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?
If the area is made one-third i.e. 1m^{2}, then the force would be:
_{}_{ }
A girl is wearing a pair of flat shoes. She weighs 550N. The area of contact of one shoe with the ground is 160cm^{2}. 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?
Force, F= 550N
Area of contact of one shoe =160 cm^{2} =160 x 10^{-4}m^{2}
Area of contact with two shoes =160 x 2 =320 cm^{2}=320 x 10^{-4}m^{2}
(a) If the girl stands on two feet,
(b)
If she stands on one foot,
Calculate the density of an object of volume 3 m^{3} and mass 9kg. State whether this object will float or sink in water. Give reason for your answer.
Volume =3m^{3}
Mass = 9kg
_{}
And density of water = 1000kg/m_{3}
The object will float in the water as the density of the object is less than the density of water.
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.
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.
(a) Write down an equation that defines density.
(b) 5kg of material A occupy 20 cm^{3} whereas 20kg of material B occupy 90cm^{3}.Which has the greater density: A or B? Support your answer with calculations.
(a)
_{}
(b)
For material A:
Mass= 5kg
Volume =20 cm^{3} = 20 x 10^{-6}m^{3}
For material B:
Mass =20kg
Volume =90 cm^{3} = 90x 10^{-6}m^{3}
Density of material A is more than density of material B.
(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 600kg of water. How much is the buoyant force acting on the boat in newton? (g=10m/s^{2})
(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.
(a) State the principle of floatation.
(b) A floating boat displaces water weighing 6000 newton.
(i)What is the buoyant force on the boat?
(ii)What is the weight of the boat?
(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
(a) Define density. What is the SI unit of density?
(b) Define relative density. What is the SI unit of relative density?
(c) The density of turpentine is 840kg/m^{3}. What will be its relative density? (density of water=1000kg/m^{3})
(a) The density of a substance is defined as mass of the substance per unit volume.
_{}
SI unit of density is kg/m^{3}.
(b) Relative density of a substance is the ratio of its density to that of water.
_{}
Relative density has no units as it is a ratio of two similar quantities.
(c) Density of turpentine =840kg/m^{3}
Density of water=1000kg/m^{3}
_{}
(a) Define pressure.
(b) What is the relation between pressure, force and area?
(c) Calculate the pressure when a force of 200N is exerted on an area of:
(i)10 m^{2}
(ii)5 m^{2}
(a) Pressure is the force acting perpendicularly on a unit area of the object.
(b)
_{}
(c) (i) Pressure on an area of 10 m^{2}
Force =200N
_{}
(ii) Pressure on an area of 5 m^{2}
Force =200N
_{ }_{}
Chapter 3 - Gravitation Exercise 126
(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 liquid?
(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.
(a) How does a boat float in water?
(b) A piece of steel has a volume of 12cm^{3}, and a mass of 96 g. What is its density:
(i) In g/cm^{3}?
(ii) In kg/m^{3}?
(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 = 12cm^{3}
_{}
_{}
(ii) Mass = 96 x 10^{-3}kg
Volume =12 x 10^{-6}m^{3}
_{}
_{}
An elephant weighing 40,000N stands on one foot of area 100cm^{2} whereas a girl weighing 400N is standing on one 'stiletto' heel of area 1 cm^{2}.
(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?
Weight of elephant=40000N
Area of one foot =1000 cm^{2}= 1000 x 10^{-4}m^{2}
Weight of girl=400N
Area of heel of girl =1 cm^{2}=1 x 10^{-4}m^{2}
(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 =1000cm^{2}= 1000 x 10^{-4}m^{2}
_{}
(c) Weight of the girl = 400N
Area of heel of girl = 1 cm^{2} = 1 x 10^{-4}m^{2}
_{ }
_{ }
(d) Girl exerts a larger pressure on the ground.
(e)
The pressure exerted by girl is 10 times greater than that exerted by the elephant.
Chapter 3 - Gravitation Exercise 127
If two equal weights of unequal volumes are balanced in air, what will happen when they are completely dipped in water? Why?
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.
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.
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.
A body floats in kerosene of density 0.8 x 10^{3}kg/m^{3} up to a certain mark. If the same body is placed in water of density 1.0 x 10^{3} kg/m^{3}, will it sink more or less? Give reason for your answer.
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.
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.
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.
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?
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.
Chapter 3 - Gravitation Exercise 128
A beaker full of water is suspended from 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?
(a) 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.
When a golf ball is lowered into a measuring cylinder containing water, the water level rises by 30cm^{3} when the ball is completely submerged. If the mass of ball in air is 33g, find its density.
Volume of golf ball = rise in water level = 30 cm^{3}
A boy gets into a floating boat.
(a) What happens to the boat?
(b) What happens to the weight of water displaced?
(c) What happens to the buoyant force on the boat?
(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.
A half kg sheet of tin sinks in water but if the same sheet is converted into a box or boat, it floats. Why?
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.
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