Chapter 09 Gravitation Exercise
Exercises
1. How does the force of gravitation between two objects change when the distance between them is reduced to half?
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Answer
Consider the Universal law of gravitation,
According to that law, the force of attraction between two bodies is
Where,
Given that the distance is reduced to half then,
Therefore once the space between the objects is reduced to half, then the force of gravitation will increase by fourfold the first force.
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?
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Answer
All objects fall from the top with a constant acceleration called acceleration due to gravity (g). This is constant on earth and therefore the value of ‘g’ doesn’t depend on the mass of an object. Hence, heavier objects don’t fall quicker than light-weight objects provided there’s no air resistance.
3. What is the magnitude of the gravitational force between the earth and a
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Answer
From Newton’s law of gravitation, we know that the force of attraction between the bodies is given by
Here
Radius of Earth
By substituting all the values in the equation
This shows that Earth exerts a force of
4. The earth and the moon are attracted to each other by gravitational force. Does the earth attract the moon with a force that is greater or smaller or the same as the force with which the moon attracts the earth? Why?
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Answer
The earth attracts the moon with a force same as the force with which the moon attracts the earth. However, these forces are in opposite directions. By universal law of gravitation, the force between moon and also the sun can be
Where,
5. If the moon attracts the earth, why does the earth not move towards the moon?
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Answer
According to the universal law of gravitation and Newton’s third law, we all know that the force of attraction between two objects is the same, however in the opposite directions. So the earth attracts the moon with a force same as the moon attracts the earth but in opposite directions. Since earth is larger in mass compared to that of the moon, it accelerates at a rate lesser than the acceleration rate of the moon towards the Earth. Therefore, for this reason the earth does not move towards the moon.
6. What happens to the force between two objects, if
(i) the mass of one object is doubled?
(ii) the distance between the objects is doubled and tripled?
(iii) the masses of both objects are doubled?
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Answer
(i)
According to universal law of gravitation, the force between 2 objects
If the mass is doubled for one object.
(ii)
If the distance between the objects is doubled and tripled
If it’s doubled
Hence,
Force thus becomes one-fourth of its initial force.
Now, if it’s tripled
Hence,
Force thus becomes one-ninth of its initial force.
(iii)
If masses of both the objects are doubled, then
7. What is the importance of universal law of gravitation?
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Answer
The universal law of gravitation explains many phenomena that were believed to be unconnected:
(i) The motion of the moon round the earth
(ii) The responsibility of gravity on the weight of the body which keeps us on the ground
(iii) The tides because of the moon and therefore the Sun
(iv) The motion of planets round the Sun
8. What is the acceleration of free fall?
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Answer
Acceleration due to gravity is the acceleration gained by an object due to gravitational force. On Earth, all bodies experience a downward force of gravity which Earth’s mass exerts on them. The Earth’s gravity is measured by the acceleration of the freely falling objects. At Earth’s surface, the acceleration of gravity is
9. What do we call the gravitational force between the earth and an object?
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Answer
The gravitation force between the earth and an object is called weight. Weight is equal to the product of acceleration due to the gravity and mass of the object.
10. Amit buys few grams of gold at the 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
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Answer
The weight of a body on the earth’s surface;
W = mg (where m = mass of the body and g = acceleration due to gravity)
The value of g is larger at poles when compared to the equator. So gold can weigh less at the equator as compared to the poles.
Therefore, Amit’s friend won’t believe the load of the gold bought.
11. Why will a sheet of paper fall slower than one that is crumpled into a ball?
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Answer
A sheet of paper has a larger surface area when compared to a crumpled paper ball. A sheet of paper will face a lot of air resistance. Thus, a sheet of paper falls slower than the crumpled ball.
12. Gravitational force on the surface of the moon is only
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Answer
Given data:
Acceleration due to earth’s gravity
Object’s mass,
Acceleration due to moon gravity
Weight on the earth
Weight on the moon
Weight
So
13. A ball is thrown vertically upwards with a velocity of
(i) the maximum height to which it rises,
(ii) the total time it takes to return to the surface of the earth.
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Answer
Given data:
Initial velocity
Final speed
Acceleration due to earth gravity
By third equation of motion,
Total time
Also,
Therefore
14. A stone is released from the top of a tower of height
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Answer
Given data:
Initial velocity
Tower height
Consider third equation of motion
15. A stone is thrown vertically upward with an initial velocity of
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Answer
Given data:
Initial velocity
Max height final velocity
Consider third equation of motion
Maximum height
Total Distance
Total Distance
Total displacement
16. Calculate the force of gravitation between the earth and the Sun, given that the mass of the earth
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Answer
Given data:
Mass of the sun
Mass of the earth
Gravitation constant
Average distance
Consider Universal law of Gravitation
17. A stone is allowed to fall from the top of a tower
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Answer
Given data:
(i) When the stone from the top of the tower is thrown, Initial velocity
Distance travelled
Time taken
Therefore,
(ii) When the stone is thrown upwards,
Initial velocity
Distance travelled
Time taken
From equations (a) and (b)
After 4sec, two stones will meet
From (a)
Putting the value of
This means that after
18. A ball thrown up vertically returns to the thrower after
(a) the velocity with which it was thrown up,
(b) the maximum height it reaches, and
(c) its position after
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Answer
Given data:
Total time
From first equation of motion:-
The velocity with which stone was thrown up is
(b) From second equation of motion
The maximum height stone reaches is
(c) In
Distance travelled in another
The distance travelled in another
Therefore in
19. In what direction does the buoyant force on an object immersed in a liquid act?
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Answer
The buoyant force on an object that is immersed in a liquid will be in a vertically upward direction.
20. Why does a block of plastic released under water come up to the surface of water?
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Answer
The density of plastic is lesser than that of water. Therefore, the force of buoyancy on plastic block will be greater than the weight of plastic block. Hence, the acceleration of plastic block is going to be in the upward direction. So, the plastic block comes up to the surface of water.
21. The volume of
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Answer
To find the Density of the substance the formula is
Density
Density
Density of water
Density of the substance is greater than density of water. So the substance will sink.
22. The volume of a
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Answer
Density of sealed packet
Density of sealed packet is greater than density of water
Therefore the packet will sink.
Considering Archimedes Principle,
Displaced water volume
Volume of water displaced
Therefore displaced water mass
Mass of displaced water