PSEB Solutions for Class 9 Science Chapter 10 Gravitation

PSEB Solutions for Class 9 Science Chapter 10 Gravitation

PSEB 9th Class Science Solutions Chapter 10 Gravitation

→ Everybody in this universe attracts every other body towards it with a force called Force of Gravitation.

→ The revolution of the moon around the earth and the falling down of a body projected upward is due to the force of gravitation.

→ Gravitation is a weak force unless it may not involve bodies having greater masses. The attractive force due to earth is called the force of gravity.

→ The law of gravitation is a universal law which means that this law applies to all big and small objects.

→ The acceleration produced in the body due to the force of gravity is called acceleration due to gravity. It is denoted by ‘g’.

→ The value of ‘g’ is more on the poles than on the equatorial line.

→ The Force of gravity decreases with the increase of height above the surface of the earth.

→ The quantity of matter present in a body is called the mass of the body.

→ Mass is the measure of inertia of the body.

→ The mass of a body remains constant at all places.

→ The weight of a body is the force with which the body is attracted towards the centre of the earth.

→ The weight of an object depends upon the product of its mass (m) and the acceleration due to gravity (g). i.e. Weight (W) = mass (m) × acceleration due to gravity (g)

→ Force acting perpendicular to the surface of an object is called thrust.

→ SI unit of pressure is Nm^-2 (or N/m²) or pascal (Pa).

→ The pressure exerted on an enclosed liquid is transmitted equally in all directions.

→ All bodies when immersed in liquid experience an upward force called upthrust or buoyant force.

→ The value of Buoyant force depends upon the density of the liquid.

→ If the weight of an immersed body is more than the upthrust then the body sinks in the liquid.

→ Those bodies float which has a density less than the density of the liquid in which they are immersed.

→ Those bodies, which have a density more than the density of the liquid in which it is immersed sink.

→ Archimedes’ principle states that when a solid body is wholly or partly immersed in a liquid then the body experiences an upward thrust due to liquid displaced by the immersed part of the body.

→ According to Archimedes’ principle when a solid body is completely or partially immersed in a liquid and the weight of the body is equal to the weight of the liquid displaced by the immersed part of the body then the body floats.

→ Kepler gave the following three laws which govern the motion of the planets:

• The planetary path of each planet is elliptical at the centre of which the sun is situated.
• The line joining sun and the planet sweeps equal areas in equal intervals of time.
• The cube of the average distance ‘r’ of a planet from the sun is inversely proportional to the square of the orbital period ‘T’ of that planet.

→ Law of gravitation states that the force of attraction between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres. This force always acts along the line joining the centres of two objects.

→ Force of Gravitation: It is that force with which two bodies attract each other but they are lying apart.

→ Acceleration due to Gravity: Acceleration produced in the bodies falling freely under the action of gravity is called acceleration due to gravity.

→ Force of Gravity: It is the force with which earth attracts all bodies towards its centre.

→ Weight: The force with which the earth attracts bodies towards it is called weight.

→ Mass: The quantity of matter contained in the body is called it’s mass.

→ Inertial Mass: This mass measures the resistance which is produced due to a change in the position of rest or motion.

→ Universal Gravitational Constant: It is the force that acts between two bodies each of unit mass and lying unit distance apart.

→ Kepler’s first law: All planets move around the sun in elliptical orbits.

→ Kepler’s second law: The line joining planet and sun sweeps out equal area in equal intervals of time.

→ Kepler’s third law: Cube of mean distance ‘r’ of the planet from the sun is proportional to the square of its orbital period.

→ Thrust: The total force acting perpendicular to the surface of the body is called thrust.

→ Buoyant Force: The upward thrust applied by the liquid on the immersed body is called Buoyant force.

→ Pressure: Thrust acting per unit area of the surface in contact is called pressure.

→ Relative Density: Relative density of a substance is defined as the ratio of the density of the substance to the density of the same volume of water. Since it is the ratio of two similar quantities, therefore it is only a number. It is also called the specific gravity of the substance.

→ Archimedes Principle: This principle states that whenever a solid body is immersed in a liquid either wholly or partly then it experiences an upward thrust due to the displaced liquid.

→ The universal law of Gravitation: The mutual force of attraction between every two bodies in this universe is directly proportional to the product of the masses of the two bodies and inversely proportional to the square of the distance between them. This force acts along the line joining the centres of the two bodies.

PSEB 9th Class Science Important Questions Chapter 10 Gravitation

Long Answer Type Questions:

Question 1.
Define Newton’s universal law of gravitation and establish mathematical formula for force of attraction between two objects.
Answer:
Newton’s universal law of gravitation-Every particle in this universe attracts each and every particle, the force of attraction is:
1. directly proportional to the product of both the masses.
2. Inversely proportional of the square of the distance between the two. This force always acts along the line joining the two masses.

Derivation of Mathematical Formula: From the fig. Jet there are two balls A and B having masses m₁ and m₂ distance between them is ‘r’.
According to Newton’s third law of motion ball A exerts a force FAB on the ball B and ball B exerts a force FBA on the ball A. These forces are equal and opposite

where G is universal gravitational constant. This is named so since its numerical value remains constant in whole of the universe and the formula is known as Newton’s universal law’ of gravitation.
Value of G
G = 6.67 × 10^-11 Nm²/kg²

Question 2.
Write Kepler’s law in context with the motion of planets.
Answer:

By the 16th centuary, a lot of data on the motion of planets had been collected by many astronomers. Johannes Kepler derived three law s based on these data. These are known as Kepler’s laws. These are:
1. Law of orbits (First laws): The orbit of a planet is an ellipse and the sun is at one of the foci, as shown in fig. In this fig. Sun is shown at O.

2. Law of area (Second laws): The line joining the planet and sun sweep equal areas in equal interv als of time. Thus, time taken for the motion from A to B is same as for the motion from C to D and area OAB and OCD are equal.

3. Law of time period (Third law): The cube of mean distance of a planet from the sun is directly proportional to square of its orbital time period
T² ∝ r³
But Kepler could not give a theory which explained the motion of planets.
Newton showed that due to motion of planets sun exerts force of gravtation on them.
i.e. T²/r³ = constant.

Question 3.
How did Robert Boyle proved experimentally that all bodies fall in vacuum with same acceleration?
Or
How did Robert Boyle show experimentally that a coin and a piece of paper when dropped simultaneously from same height in vacuum fall with same acceleration?
Answer:
Boyle’s Experiment: As shown in fig. Robert Boyle took a long glass tube. A heavy coin and a piece of paper were placed inside the tube. The ends of the tube were closed. Air from the tube was removed with the help of a vacuum pump.

When the tube was quickly inverted it was seen that coin and a piece of paper hit the bottom of the tube at the same time. Now the experiment was repeated with air inside the glass tube. This time it was observed that a piece of paper falls slowly whereas the coin immediately hit the bottom of glass tube. This experiment proves that in vacuum all bodies irrespective of their masses (both light and heavy) fall towards earth with same acceleration

Question 4.
(a) Prove that acceleration due to gravity is independent of mass.
(b) Find the value of ‘g’.
Answer:
(a) Consider a body of mass ‘m’ lying on the surface of earth. Suppose M and R are respectively mass and radius of earth.
Let F be the force of gravity acting on the body

Question 5.
Describe those factors which are responsible for variation in the value of acceleration due to gravity ‘g’?
Answer:
Variation in the value of acceleration due to following factors:
Variation in g with altitude-Value of ‘g’ is maximum on the surface of earth. As we move in the upward direction (higher altitudes) value of ‘g’ goes on decreasing. We can calculate value of ‘g at altitude using mathematical formula. If
g_e = acceleration due to gravity on the surface of earth
g_h = acceleration due to gravity at height h
R = radius of earth

Question 6.
Establish the relation between ‘g’ and ‘G’.
Or
Deduce an expression for it in terms of mass of the earth ‘M’ and universal gravitational constant ‘G’.
Or
Show that the acceleration due to gravity of an object is independent of its mass.
Answer:

Relation between ‘g’ and ‘G’. Suppose the earth is a sphere of mass M and radius R, Consider a body of mass m lying at a distance ‘r’ from the centre of the earth. According to Newton’s law of gravitation, the force of attraction between the earth and the body,

Question 7.
What is Archimedes principle? How can you verify it experimentally? Also write applications of Archimedes principle.
Answer:
Archimedes Principle: According to this principle when a solid body is immersed either completely or partially in a liquid, it experiences an upward thrust which is equal to the weight of the liquid displaced by the immersed part of the body.”

Experimental Verification: Take a stone piece and tie it to the hook of a spring balance. Hold the spring balance in your hand or support it from the stand so as to suspend the stone piece as shown in fig.

Note, the reading on the spring balance to know the weight of the stone. Now pour some water a beaker with and slowly immerse the stone in the water while remaining tied with the hook of spring balance as shown in fig. (b). You will see that spring balance shows a decreased reading i.e. weight of stone is decreased after it is immersed in the water.

Subtract the two readings to know the decrease in the weight of stone. As soon as the stone is immersed in the water it displaces water equal to its own volume. Collect this water in other beaker and measure its weight. You will find that this weight of water is equal to the decrease of weight of the stone. Thus Archimedes principle is proved.

Applications of Archimedes’ Principle:

1. Archimedes principle is used in designing ships and submarines.
2. Lactometers are constructed on Archimedes’ Principle which are used to measure puritv of a sample of milk.
3. Hydrometers used to measure density of liquid are also based on Archimedes principle.

Short Answer Type Questions:

Question 1.
Which one is greater-the gravitational force of the earth on 1 kg iron or the force of gravitation applied by 1 kg on earth?
Answer:
According to Newton’s law of Gravitation there exists of mutual force of attraction between two objects. Since the mass of iron is less than the mass of the earth, therefore earth attracts 1 kg mass towards it with a greater force which is noticeable.

Question 2.
Why is G called universal gravitational constant?
Answer:
G is called universal gravitational constant because its numerical value is same in the whole universe. This value is G = 6.67 x 10^-11 Nm²/kg².

Question 3.
Is the value of ‘g’ at a given place same for different bodies or it is variable?
Answer:

Question 4.
Why does a body becomes weightless at the centre of earth?
Answer:
We know value of g goes on decreasing as we continue moving deep into the earth and value of acceleration due to gravity (g) = 0 at the centre of earth. Thus, a body whose mass is m,
Weight of body = m × 0 = 0
Therefore, body becomes weightless.

Question 5.
A tennis ball jumps higher at hills than at planes. Explain.
Answer:
Value of g decreases with altitude, thus gravitational force acting on ball at hills is less as a result ball jumps higher at hills than at planes.

Question 6.
The weight of an object on the surface of earth is 9.8 N. What does this statement mean?
Answer:
We know that value of ‘g’ on the surface of earth is 9.8 m/s² and the relation for weight of an object is:
w = m × g
9.8 = m × 9.8
or m = 9.8/9.8
∴ m = 1 kg
The given statement therefore means the mass of the object on earth is 1 kg.

Question 7.
What type of motion a freely falling body execute under gravity?
Answer:
A body falling freely under gravity executes uniform accelerated motion. If bodies with different masses and different shapes are allowed to fall freely in vacuum, they all will have same acceleration due to gravity.

Question 8.
Give points of difference between Acceleration due to gravity (g) and Universal gravitational constant'(G).
Answer:
Difference between g and G:

Acceleration due to gravity (g)	Gravitational constant (G)
1. It represents acceleration acquired by the body due to gravity.	It represents force of attraction between two masses of 1 kg each lying 1 m apart.
2. Its value is different at different places on earth surface.	Its value is constant at all places. Thus, it is called universal constant.
3. Its value at the surface of earth is 9.8 m/s2.	Its value is 9.67 × 10-11 Nm2kg-2.
4. It is a vector quantity.	It is a scalar quantity.

Question 9.
You buy W weight of sugar at a place situated on equitorial line and then take it to Antarctica. Will that sugar weigh same there? If not whether it would be more or less.
Answer:
The value of ‘g’ at Antarctica is not same as on equator. The value of ‘g’ increases on Antarctica therefore, sugar bought at any place on equitorial line when taken to Antarctica would have more weight but its mass will remain the same because mass is a constant quantity.

Question 10.
Why cannot we move a finger without disturbing all the stars?
Answer:
When we move our finger, then distance between finger and all other things in the universe change and as a result force of gravitation also changes. Thus, all the things get disturbed, although this disturbance is negligible.

Question 11.
Distinguish between Gravitation and Gravity.
Answer:

• Gravitation: Gravitation is the force of attraction between any two bodies in the universe. The attraction between the sun and the earth, the attraction between a table and a chair are examples of gravitation.
• Gravity: Gravity is a special case of gravitation when one of the two bodies is the earth. Gravity is the attraction between the earth and any object lying on or near its surface. A ball thrown upward falls back on the surface of the earth due to earth’s force of gravity.

Question 12.
Explain why a small piece of stone is not attracted towards another big place of stone on the earth’s surface?
Answer:
Because of very small value of G, the force of attraction between any two such ordinary sized bodies is so small that it cannot produce motion in them.

Question 13.
The earth attracts an apple. Does the apple also attract with earth? If it does, why does the earth not move towards the apple?
Answer:
The apple also attracts the earth with an equal and opposite force. The mass of the earth is very large compared to that of apple. So, the acceleration produced in earth is very small as compared to that in the apple. Hence, the motion of the earth towards the apple is not appreciable and therefore, is not noticeable.

Question 14.
If the force of gravity somehow vanishes today, why would we be sent being in space?
Answer:
In the absence of force of gravity, the centripetal force required to keep us rotating along the earth would not be available. As a result would fly off along the tangent to with into the space.

Question 15.
What is meant by density and relative density?
Answer:

Question 16.
What do you mean by buoyancy and centre of buoyancy? In which direction does the buoyant force on an object immersed in a liquid act?
Answer:
Buoyancy: When a body is immersed partially or wholly in a fluid (liquid or gas), it displaces fluid. The displaced fluid exerts an upward force on the body.

The upward force acting on a body imnu rsed in a fluid is called upthrust or force of buoyancy and the phenomenon is called buoyancy. The buoyancy acts through the centre of gravity of the displaced fluid which is called centre of buoyancy.

Question 17.
State Archimedes’ principle.
Answer:
Archimedes’ Principle. When a solid body is immersed completely or partially in a fluid, it experiences an upward thrust which is equal to the weight of the fluid displaced by the immersed part of the body.

Question 18.
Name two forces which act on a body immersed in a liquid. Give the directions in which they act.
Answer:
Two forces which act on a body immersed in a liquid are:

• Weight of the body acting downward.
• An upthrust due to displaced liquid.

Question 19.
How is submarine able to move on water surface as well as go under water?
Answer:
To move submarine under water, water is pumped in its special tanks. This causes a net increase in weight and thus submarine goes down in water.

To bring the submarine upon the surface of sea, the water from the tanks is thrown out by pumps. When water from the tanks of submarine is taken out, the net weight of the submarine decreases without any change in its volume and it comes up on the surface of water.

Question 20.
Give reason when Big buildings and dams have wide foundations for safety.
Answer:
Dams and big buildings have wide foundations for safety, because they may not collapse under high pressure of the building.

Question 21.
A steel needle sinks in water but a steel ship floats. Explain how?
Answer:
A steel needle sinks in water because it displaces less weight of water which provides less buoyant force than the actual weight of the needle. On the other hand, steel ship floats because it displaces a large weight of water which provides a greater buoyant force to keep it a float.

Question 22.
Give reasons for the following :
(a) A sharp blade is more effective in cutting an object than a blunt blade.
(b) A cork piece floats but an iron piece sinks in water.
Answer:
(a) We know Pressure =  Thrust/Area . For the given thrust, pressure ∝  1/Area . Thus the effect of the same magnitude of force is more when the area of surface in contact is less. Hence a sharp blade is more effective in cutting an object than a blunt blade.
(b) The density of the cork piece is less than the density of water, and the. density of the iron piece is more than the density of water. Hence, the cork piece floats but the iron piece sinks in water.

Question 23.
Explain the following:
(a) Swimmers are provided with an inflated rubber jacket.
(b) It is easier of swim in sea water than in river water.
Answer:
(a) Swimmers are provided with an inflated rubber jacket to increase the volume such that density is decreased, which is helpful for swimming.
(b) It is easier to swim in sea water than in river water because density of sea water is more than water of the needle sinks in a river while a ship float on it.

Question 24.
Why is the pressure on ground more when a man is walking than when he is standing?
Answer:
When the man stands he exerts a force on the ground equal to his own weight. But when he walks, he pushes the ground backward and exerts an additional force on the ground. That is why pressure on the ground is more when a man is walking than when he is standing.

Question 25.
Why a bucket of water is lighter when in water than when it is taken out of water?
Answer:
Inside water, the bucket experiences upthrust exerted by displaced water, so its apparent weight becomes less than the actual weight. When bucket is taken out of water, upthrust on the bucket disappears and it feels heavier.

Question 26.
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 floats. Why?
Answer:
The average density of a fresh egg is more than that of pure water but less than that water in which salt is dissolved. So a fresh egg sinks in pure water while it floats in salty water.

Important Formulae:

Necessary Data-
Earth
Mass = 6 × 10²⁴ Kg
Radius = 6.4 × 10⁶ m (6400 Km)
Distance from Sun = 1.5 × 10¹¹ m
Moon
Mass = 7.3 × 10²² Kg

Numerical Problems (Solved):

Question 1.
Two spheres of 1 kg mass each are separated by 3 m. Calculate the gravitational force between then. Given G = 6.67 × 10^-11 Nm²/kg².
Solution:
Here m₁= m₂ = 1 kg
Distance between two spheres, (r) = 3 m
Gravitational constant (G) = 6.67 × 10^-11 Nm²/kg²
We know

Question 2.
The radius of moon is 1.7 × 10⁶ m and its mass is 7.35 × 10²² kg. What is the acceleration due to gravity on the surface of moon? Given G = 6.67 × 10^-11 Nm²/kg²
Solution:
Radius of moon, (R) = 1.7 × 10⁶ m
Mass of moon, (M) = 7.35 × 10²² kg
Gravitational constant, (G) = 6.67 × 10^-11 Nm²/kg² (Given)
We know, Acceleration due to gravity on moon

Question 3.
Find the change in weight percentage of a body when it is taken from equator to poles. Polar radius is 6357km and equitorial radius is 6378km.
Solution:
Polar radius, (r) = 6357 km
Equitorial radius (R) = 6378 km
∴ h = R – r
⇒ h = (6378 – 6357)km
h = 21km
R = 6400 km(Approx)

Question 4.
At what height above the earth surface, the acceleration due to gravity will be half that on the surface of earth? Suppose R is the radius of earth.
Solution:
Let h be the height above earth surface where

Question 5.
A ball is dropped from top of 40 m high tower. What will be its velocity after covering a distance of 20 m ? What will be its velocity on striking the earth?
Answer:
1. Here, height of the tower, (h) = 40 m
Initial velocity, (u) = 0
Acceleration due to gravity, (g) = 10m/s²
Distance covered (S) = 20m

i.e. Velocity of ball when it strikes the earth. = 20 m/s

Question 6.
If weight of an object is 49 N then what will be its mass?
Solution:
Weight of the object W = 49 N
g = 9.8 m s^-2
We know, weight = Mass × acceleration due to gravity
W = m × g
49 = m × 9.8
or m = 49/9.8
∴ m = 5 kg

Question 7.
Ah object is projected vertically upward with a velocity of 50 m/s. After what time the object will attain the maximum height.
Solution:
Initial velocity of the object (u) = 50 m/s [upward direction]
Acceleration due to gravity, (g) = – 10 ms^-2 [object comes to rest]
Velocity of the object at maximum height,
(υ) = 0
Time taken (t) =?
We know, υ = u + gt
0 = 50 + (-10) × t
0 = 50 – 10t
or 10t = 50
∴ t = 50/10 = 5s
So the object will attain its maximum height after 5 seconds.

Question 8.
A stone is dropped from the edge of a rooftop. If it crosses 2 m high window in 0.1 second then what is the distance between the upper end of window and the roof?
Solution:

Distance covered in crossing the window
(S) = 2 m
g = 9.8 ms^-2
t = 0.1 s
Let υ be the velocity of the stone when it reaches the upper edge A of the window.

Question 9.
A helicopter drops food packet for people caught in stationary boat. This is moving at a height of 20 m with a horizontal velocity of 2 m/s. When food packet is dropped the nearest end of the boat is just below the helicopter. If boat is 5 m long shall people caught in the boat receive the dropped food packets?
Solution:

Question 10.
An object of volume V is immersed in a liquid of density ρ. Calculate the magnitude of buoyant force acting on the object due to the liquid.
Solution:
By Archimedes’ principle, the magnitude of buoyant force,
U.F. = Weight of liquid displaced = Volume × Density × g or
or U.F. = Vρg

Question 11.
The pressure exerted by the weight of a cubical block of side 4 cm on the surface is 10 pascal. Calculate the weight of the block.
Solution:
Here pressure exerted, P = 10 pascal = 10 Nm^-2,
Area, A = 4 cm × 4 cm
= 16 × 10^-4 m²
As P = F/A
= W/A
W = P × A
= 10 Nm^-2 × 16 × 10^-4m²
= 1.6 × 10^-2 N

Question 12.
The volume of a 500 g sealed packet is 350 cm³. Will the packet float or sink in water if the density of water is 1 g cm^-3? What will be the piass of the water displaced by this packet?
Solution:

Since its density (1.43 g cm^-3) is more than that of water (1 g cm^-3) thus, the sealed packet will sink in water
Volume of water displaced = Volume of packet
= 350 cm³
Mass of water displaced = Volume × Density
= 350 cm³ × 1gcm^-3
= 350 g

Question 13.
A block of wood is kept on the table top. The mass of wooden block is 5 kg and its dimensions are 40 cm × 20 cm × 10 cm. Find the pressure exerted by the wooden block on the table top if it is made to lie on the table top with its sides of dimensions (a) 20 cm × 10 cm and (b) 40 cm × 20 cm.
Solution:
Here, M = 5kg and g = 9.9 ms^-2
Weight = force exerted on table top
= mg
= 5 × 9.8
= 49 N

Question 14.
A solid body floating in water has 1/6th of its volume above the surface.
What fraction of its volume will project upwards if it floats in a liquid of density 1,020 km m^-3?
Solution:

Very Short Answer Type Questions:

Question 1.
What is g on the moon as compared to that on earth?
Answer:
Nearly 1/6th of its value on earth.

Question 2.
What is unit of G?
Answer:
It is Nm² kg^-2.

Question 3.
What is the mass of the earth?
Answer:
It is about 6 × 10²⁴ kg.

Question 4.
What is essential property of matter-mass or weight?
Answer:
Mass is the basic and essential property. It is constant everywhere. Weight of a body varies from place to place.

Question 5.
What is SI unit of weight of a body?
Answer:
It is newton (N).

Question 6.
The earth’s gravitational force causes an acceleration of 5 m s^-2 on a 1 kg mass somewhere in the space. How much will be the acceleration of a 3 kg mass at that place?
Answer:
Same i.e., 5ms^-2 since g at a place is independent of mass of the body.

Question 7.
Why one can jump higher on the surface of moon than on the earth?
Answer:
The g at moon surface is nearly 1/6th of that at the surface of earth. Hence one can jump six times higher on the moon with a given initial velocity.

Question 8.
Give the value of universal gravitational constant in S.I. units.
Answer:
(G) = 6.67 × 10^-11 Nm²/kg²
The value of gravitational constant.

Question 9.
The value of ‘G’ on the surface of earth is 6.67 × 10^-11 Nm²/kg². What is its value on the surface of moon?
Answer:
Since G is universal constant so its value on moon surface will be same as on the earth surface i.e. G = 6.67 × 10^-11 Nm²/kg² .

Question 10.
State two factors on which the gravitational force between two objects depends.
Answer:
The gravitational force between two objects depends on: (i) their masses (ii) distance between them.

Question 11.
Write the formula to find the magnitude of gravitational force between the earth and an object on the surface of the earth.
Answer:

Question 12.
Can the mass of a body be zero.
Answer:
No, mass of body can never be zero.

Question 13.
Mass of an object on the earth is 600g. What will be its mass on moon?
Answer:
Mass of the object on moon will be same i.e. 600 g.

Question 14.
You find your mass to be 42 kg on a weighing machine. Is your mass more or less than 42 kg?
Answer:
Mass is a constant quantity. So, it can not be more or less than 42 kg.

Question 15.
How does the value of ‘g’ vary from equator to poles?
Answer:
The value of ‘g’ increases as we move from equator to poles.

Question 16.
What will be the weight of an object on the earth whose mass is 10 kg?
Answer:
Weight of the object on earth
(W) = m x g
= 10 kg × 10 m s^-2
= 100 N

Question 17.
Write the S.I. unit of G.
Answer:
Nm²/kg².

Question 18.
When does an object float when placed on the surface of water?
Answer:
If the density of object is less than water, it will float.

Question 19.
While swimming why do we feel light?
Answer:
The swimmer experiences an upward force by water, this causes buoyancy and makes the swimmer feel light.

Question 20.
Why does a truck or a motor-bus has much wider tyres?
Answer:
So that pressure acting on the road due to weight of truck or motor-bus may be small.

Question 21.
An army tank weighing more than a hundred tonne move conveniently on an earthen road. How?
Answer:
The army tank rests upon a continuous broad chain. So, the total surface area is large and pressure on road due to weight of tank is not very high.

Question 22.
What is the unit of relative density? Why?
Answer:
Relative density has no unit because it is a ratio of two terms having same units. So relative density is expressed in numbers only.

Question 23.
The weight of an object on the moon is ………………. of its weight on the earth.
Answer:
The weight of an object on the moon is 1/6th of its weight on the earth.

Science Guide for Class 9 PSEB Gravitation InText Questions and Answers

Question 1.
State the universal law of gravitation.
Answer:
Newton’s universal law of gravitation. This law states that every object in the universe attracts every other object with a force which is proportional to the product of their masses and inversely proportional to the square of the distance between them. This force always acts along the line joining their centres.

If m₁ and m₂ are the masses of two objects lying distance d apart, then force F between them is:

where G is a constant, called universal gravitational constant.

Question 2.
Write the formula to find the magnitude of gravitational force between the earth and an object on the surface of the earth.
Answer:

Let ‘m’ be the mass of object on the earth and the mass of earth be ‘M’. If ‘R’ is the radius of the earth, then the formula for gravitational force between earth and object is:

Since the size of the object is very small as compared to that of the earth, therefore distance between centre of object and centre of the earth is taken to be equal to radius of the earth.

Question 3.
What is meant by Free Fall?
Answer:
Free Fall: An object is said to be in a state of free fall when it falls towards the earth under the influence of gravitational force between the object and the earth. There is no change in the direction of motion of the body but value of velocity keeps changing due to attraction of earth.
It falls towards earth with an acceleration of 9.8 m s^-2.

Question 4.
What is meant by acceleration due to gravity?
Answer:
Acceleration due to gravity: The acceleration produced in the motion of a body falling under the force of gravity is called acceleration due to gravity. It is denoted by ‘g’.

Question 5.
What is the difference between the mass of an object and its weight?
Answer:
Difference between mass and weight:

Mass	Weight
1. Mass is the quantity of matter contained in a body and is the measure of its inertia.	Weight of a body is the force with which a body is attracted towards the centre of the earth.
2. Mass of a body remains constant at all places.	Weight of a body (W = mg) changes from place to place due to the change in the value of acceleration due to gravity ‘g’.
3. Mass is a scalar quantity.	Weight is a vector quantity.
4. Mass is measured by a pan balance.	Weight of a body is measured by a spring balance.
5. Mass of a body is never zero.	Weight of a body is zero at the centre of the earth.
6. The unit of mass is kg.	The unit of weight is newton or kg-wt.

Question 6.
Why is the weight of the object on moon -th of its weight on the earth?
Answer:
We know that, Mass of earth (M_e) = 100 × Mass of moon (M_m)
Radius of earth (R_e) = 4 × Radius of moon (R_m)
Since the mass and radius of moon is less than that of the earth therefore, moon exerts lesser 1/6th force of attraction on the object. Hence the weight of the object on moon is 1/6th of the weight of the same object on earth.

Question 7.
Why is it difficult to hold a school bag having a strap made of thin and strong string? (Imp.)
Answer:
We know force per unit area is called pressure i.e. P = F/A. Now for the constant force, the pressure experienced is inversely proportional to area. Now, when the string is thin, it has less area of cross-section and hence, exerts greater pressure on the hand for the given weight of school bag. Thus, it becomes difficult to hold the school bag.

Question 8.
What do you mean by buoyancy?
Answer:
Buoyancy means upward thrust acting in a body when the body is completely or partly immersed in a fluid (i.e. liquid or a gas).

Question 9.
Why does an object float or sink when placed on the surface of water?
Answer:
When the object has density less than the density of water i.e. 1 gm/cm³ then it, floats on the surface of water, because, it displaces more weight of water than its own weight. The upward force applied by displaced water is called buoyant force. As buoyant force is more than its own weight, therefore, it floats.

When the object has a density of more than 1 gem^-3, then it sinks in water, because, it always displaces less weight of water than its own weight. As buoyant force is less than its own weight, therefore, it sinks.

Question 10.
You find your mass to be 42 kg on a weighing machine. Is your mass more or less than 42 kg?
Answer:
With a weighing machine, we find weight and not mass, Your weight as noted by the machine is 42 kg f (or 42 kg wt) and not 42 kg. The actual weight is more than 42 kg. since you have displaced some air when weighed in it. However, the mass will remain the same in all cases.

Question 11.
You have a bag of cotton and an iron bar, each indicating a mass of 100 kg when measured on a weighing machine. In reality, one is heavier than the other. Can you say which one is heavier and why?
Answer:
The bag of cotton will actually be heavier than the iron bar. Cotton is bulky and has more area as compared to the area of the iron bar. Due to more area occupied by cotton bags, it experiences more upthrust because of the displaced volume of air. This upthrust reduces the downward pull and hence its weight as recorded by the weighing machine will be lesser.

PSEB 9th Class Science Guide Gravitation Textbook Questions and Answers

Question 1.
How does the force of gravitation between two objects change when the distance between them is reduced to half?
Answer:
Let m₁ and m₂ be the masses of the two objects A and B respectively and ‘r’ be the distance between their centres. Therefore, according to the law of Gravitation, the force of attraction between them is given ahead:

Therefore, force of attraction will become four times when the distance between the two objects is reduced to half.

Question 2.
Gravitational force acts on all objects in proportion to their masses. Why then, a heavy object does not fall faster than a light object?
Solution:

Question 3.
What is magnitude of gravitational force between the earth and a 1 kg object on its surface? Take mass of earth to be 6 × 10²⁴ kg and radius of the earth is 6.4 × 10⁶ m. G = 6.67 × 10^-11 Nm² kg^-2.
Solution:
Here, mass of the object (m) = 1 kg
Mass of the earth (M) = 6 × 10²⁴ kg
Radius of the earth (R) = 6.4 × 10⁶ m
The magnitude of force of gravitation between object of mass 1 kg and the earth

Question 4.
The earth and the moon are attracted to each other by gravitational force. Does the earth attracts the moon with a force that is greater than or smaller than or the same as the force with which the moon attracts the earth? Why?
Answer:
The earth attracts the moon with the same force as the force with which the moon attracts the earth. According to Newton’s third law., these two forces are equal and opposite.

Question 5.
If the moon attracts the earth, why does the earth not move towards the moon?
Answer:
According to Newton’s third law, the moon also attracts earth with a force equal to that with which the earth attracts the moon. But the earth is much larger than the moon. So, the acceleration produced in the earth (a ∝ 1/m) is very less and is not noticeable.

Question 6.
What happens to the force between two objects, if

1. the mass of one object is doubled?
2. the distance between the objects is doubled and tripled?
3. the masses of both objects are doubled?

Answer:


i.e. the force becomes four times the original force.

Question 7.
What is the importance of universal law of gravitation?
Answer:
Importance of universal law of gravitation:

1. The gravitational force between the sun and the earth makes the earth move around the sun with a uniform speed.
2. The gravitational force between the earth and the moon makes the moon move around the earth with uniform speed.
3. The high and low tides are formed in sea due to the gravitational pull exerted by the sun and the moon on the surface of water.
4. It is the gravitational pull of the earth, which holds our atmosphere in place.
5. The gravitational pull of earth keeps us and other bodies firmly on the ground.

Question 8.
What is the acceleration of free fall?
Answer:
It is the acceleration produced when a body falls under the influence of the force of gravitation of the earth alone. Near the surface of the earth, its value is 9.8 m s^-2.

Question 9.
What do we call the gravitational force between the earth and an object?
Answer:
The gravitational force between the earth and an object is called weight of the object.

Question 10.
A person ‘A’ buys few grams of gold at poles as per the instruction of one of his friends. He hands over the same when he meets him at the equator. Will the friend agree with the weight of gold bought? If not, why?
[Hint: The value of g is greater at the poles than at the equator.]

Answer:
The value of g at the equator is less than that at the poles. Hence, the few gm of gold at poles will measure less when taken to the equator. Therefore, the friend will not agree with the weight of the gold bought.

Question 11.
Why will a sheet of paper fall slower than one
Answer:
The sheet of paper will experience a larger air resistance due to its large surface area than that of its ball form.

Increased force of friction will reduce the forward driving force due to gravity. Hence sheet of paper falls slower than one that is crumbled into a ball.

Question 12.
Gravitational force on the surface of moon is 1/6th as strong as gravitational force on the earth. What is the weight in newton of a 10 kg object on moon and on the earth?
Solution:
Mass of the object on moon = 10 kg
Mass of the object on the earth = 10 kg
Acceleration due to gravity on the earth (g) = 9.8 m s^-2
Weight of the object on the earth (W) = m × g
= 10 × 9.8
= 98 N
Now weight of the object on moon’s surface = 1/6 × weight of the object on earth
= 1/6 × 98N
= 16.3 N

Question 13.
A ball is thrown vertically upwards with a velocity of 49 m s^-1. Calculate :
1. The maximum height to which it rises
2. The total time it takes to return to the surface of earth.
Solution:
1. Here initial velocity of the ball (u) = 49 m s^-1
[At maximum height the ball comes to rest]
Final velocity of the ball (υ) = 0
Acceleration due to gravity (g) = – 9.8 m s² [in the upward direction]
Time to reach the maximum height (t) =?

∴ Total time taken to return to earth = Time for upward journey + Time for downward journey
= t + t
= 2 t
= 2 × t
= 2 × 5 s
= 10 s

Question 14.
A stone is released from the top of a tower of height 19.6 m. Calculate the final velocity just before touching the ground.
Solution:

Question 15.
A stone is thrown vertically upward with an initial velocity of 40 m s^-1. Taking g = 10 m s^-2, find the maximum height reached by the stone. What is the net displacement and the total distance covered by the stone?
Solution:
Initial velocity of the stone, (w) = 40 ms^-1,
Final velocity of the stone on reaching maximum height (υ) = 0 [At rest]
Acceleration due to gravity, (g) = – 10 m s² [upward direction]
Maximum height reached, (h) = ?
We know υ² – u² = 2gh
(0)² – (40)² = 2 × (- 10) × h
– 40 × 40 = – 2 × 10 × h
∴ h = −40×40/−2×10
= 80 m
Since stone goes 80 m upwards and then returns to the point of throw by moving 80 m downward.
∴ Total distance travelled by stone = h + h
= 2 h
= 2 × 80 m
= 160 m
As the stone returns to the initial point of throw, therefore, net displacement is zero (0)

Question 16.
Calculate the force of gravitation between the earth and the sun, given the mass of earth = 6 × 10²⁴ kg and of the sun = 2 × 10³⁰ kg. Average distance between the two is 1.5 × 10¹¹ m.
Solution:
Given, mass of the earth (m₁) = 6 × 10²⁴ kg
Mass of the sun, (m₂) = 2 × 10³⁰ kg
Average distance between the earth and the sun (d) = 1.5 × 10^-11 m
G = 6.7 × 10^-11 N – m² /kg²
Force of gravitation (F) = ?
According to the universal law of gravitation,

Question 17.
A stone is allowed to fall from the top of the tower 100 m high and at the same time another stone is projected vertically upwards from the ground with a velocity of 25 m s^-1. Calculate when and where the two stones will meet? (g = 10 ms^-2)
Solution:

Height of the tower = 100 m
Suppose a stone is allowed to fall from point A at the top of tower and another stone is projected vertically upward from point C. Let us suppose that these two stones meet at point B after ‘t’ seconds.
Distance covered by first stone (AB) = x
∴ Distance covered by second stone (CB) = (100 – x)
Downward Journey of first stone
u = 0
g = + 10 m s^-2
(S) = x metres

∴ x = 16 × 5 = 80 m
i.e. the first stone will cover a distance of 80 m in the downward direction, and second stone will cover upward distance = 100 – x
= 100 – 80
= 20 m

Question 18.
A ball thrown up vertically returns to the thrower after 6 s. Find

1. Velocity with which it was thrown up,
2. the maximum height it reached; and
3. its position after 4 s.

Solution:
Total time taken (t) = 6 s
Time taken by the ball for upward joumey= Time taken by the ball for downward journey
= 6s/2
= 3 s
(i) Suppose the ball is thrown upwards with initial velocity u
g = – 9.8 m/s²
t = 3 s
υ = 0 [the ball stops on reaching the maximum height]
Maximum height(S) = h
using υ = u + gt
0 = u + (-9.8) × 3
0 = u – 29.4
∴ u = 29.4 ms^-1

∴ Height of the ball from the thrower = (44.1 – 4.9) m
= 39.2 m

Question 19.
In what direction does the buoyant force on an object immersed in a liquid act.
Answer:
If an object is immersed in a liquid then the buoyant force due to displaced liquid acts on the object in vertically upward direction.

Question 20.
Why does a block of plastic immersed under water come to the surface of water?
Or
Give reason why, a block of plastic when immersed underwater comes up to the surface of water.
Answer:
As density of plastic is less than the density of water. The upward thrust applied by displaced water on the plastic will be more than the weight of the plastic. So plastic block will float on water.

Question 21.
The volume of 50 g of a substance is 20 cm³. If the density of water is 1 g cm^-3, will the substance float or sink?
Solution:

Question 22.
The volume of 500 g sealed packet is 350 cm³. Will the packet float or sink in water if the density of water is 1 g cm^-3 ? What will be the mass of the water displaced by this packet?
Solution:

But Density of water ρ_w = 1 g cm^-3
As density of sealed packet is more than that of water, the sealed packet will sink in water.
∴ Volume of sealed packet immersed in water = V = 350 cm³
Weight of water displaced by the packet = Vρ_w
= 350 × 1
= 350g.

Follow on Facebook page – Click Here

Google News join in – Click Here

Read More Asia News – Click Here

Read More Sports News – Click Here

Read More Crypto News – Click Here