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1. State the universal law of gravitation.
Ans: Universal law of gravitation states that every object in the universe attracts every other object. The gravitational force between two objects is directly proportional to their masses and inversely proportional to the square of the distance between them.
2. Write the formula to find the magnitude of the gravitational force between the earth and an object on the surface of the earth.
Ans: g = G x M / R2
3. What do you mean by free fall?
Ans: When an object falls due to the gravitational force, alone it is called free fall.
4. What do you mean by acceleration due to gravity?
Ans: The acceleration caused due to the gravitational force is called acceleration due to gravity. The S.I. unit of gravitational force is m/s2
5. What are the differences between the mass of an object and its weight?
Ans:
|
Basis |
Mass |
Weight |
|
Definition |
Mass is the actual quantity of matter of an object. |
Weight is the product of mass of object and gravity. |
|
S.I unit |
The S.I unit of mass is “Kg” |
The S.I unit of weight is “Kg” |
|
Symbol |
Mass is denoted with m |
Weight is denoted with W |
|
Formula |
Mass = weight / gravity |
Weight = mass x gravity |
6. Why is the weight of an object on the moon 1/6 th its weight on the earth?
Ans: The gravity of moon is 1/6th of the gravity of earth and hence the weight of the object is 1/6th its weight on the earth.
7. Why is it difficult to hold a school bag having a strap made of a thin and strong string?
Ans: The strap made of thin and strong string will increase the pressure on the shoulder that would make it difficult to carry the bag.
8. What do you mean by buoyancy?
Ans: Buoyancy is the property of fluid that exerts an upward pressure on object, which is immersed into it.
9. Why does an object float or sink when placed on the surface of water?
Ans: If the density of an object is more than the density of the water it will sink in water whereas if the density of object is less than the density of water it will float on water.
10. You find your mass to be 42 kg on a weighing machine. Is your mass more or less than 42 kg?
Ans: The weight will be more than 42 kg because weighing machine measure the apparent weight.
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 other. Can you say which one is heavier and why?
Ans: As the density of cotton is less than that of iron bar, it experience more upward thrust by air as compared to iron bar, which decreases its weight significantly. Hence, the actual weight of cotton is relatively high than that of iron bar.
1. How does the force of gravitation between two objects change when the distance between them is reduced to half?
Ans: If distance between two objects is reduced to half then the gravitational force between them will increase by 4 times.
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?
Ans: Gravitational force acts on all objects in proportion to their masses but a heavy object does not fall faster than a light object because only one force i.e. gravity in acting on it.
3. What is the magnitude of the gravitational force between the earth and a 1 kg object on its surface? (Mass of the earth is 6 × 1024 kg and radius of the earth is 6.4 × 106 m.)
Ans: Given, mass of object m = 1 kg
Mass of earth M = 6 x 1024 kg
Radius of earth R = 6.4 x 106 m
Now, using G = F x R2 / (M x m)
=> F= G x M x m / R2
=> F = (6.67 x 10-11 x 6 x 1024 x 1) / (6.4 x 106)2
=> F = (40.02 x 1013) / 40.96 x 1012
=> F = 0.977 x 10
=> F = 9.77 N
Hence, the gravitational force is 9.77 N.
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?
Ans: The earth will attract the moon with same force with which the moon attracts the earth because according to universal law of gravitation the force of attraction between two objects is directly proportional to the product of their masses and inversely proportion to square of distance between them, which is constant for moon, and earth.
5. If the moon attracts the earth, why does the earth not move towards the moon?
Ans: The moon attracts the earth but the earth does not move towards the moon because the earth has greater mass than 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?
Ans: (i) if the mass of one object is doubled the force between the objects will also be doubled.
(ii) if the distance between two objects is doubled and tripled the force will be 1/4th and 1/6th respectively.
(iii) if the masses of both objects are doubled the force will increase by four times.
7. What is the importance of universal law of gravitation?
Ans: Universal law of gravitation is important for the following reasons:
8. What is the acceleration of free fall?
Ans: The acceleration of free fall will be equal to the acceleration due to gravity at that place. In case of earth, it would be 9.8 m/s2
9. What do we call the gravitational force between the earth and an object?
Ans: Gravity is the gravitational force between the earth and an 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 g is greater at the poles than at the equator.]
Ans: No, the friend will not agree with the weight of the gold because the gravity at poles is greater than the gravity at equator, which significantly reduces the weight of the gold.
11. Why will a sheet of paper fall slower than one that is crumpled into a ball?
Ans: A sheet of paper has greater surface than paper crumpled into a ball due to which it faces more air resistance that reduces its speed and hence it fall slower.
12. Gravitational force on the surface of the moon is only 1/6 as strong as gravitational force on the earth. What is the weight in newtons of a 10 kg object on the moon and on the earth?
Ans: Given, the mass of object = 10 kg
The weight of object on earth W = m x g
=> W = 10 x 9.8
=> W = 98 N
The acceleration due to gravity at moon = 1/6 x 9.8 = 1.63 m/s2
So, the weight of object on moon = 10 x 1.63 = 16.3 N
13. A ball is thrown vertically upwards with a velocity of 49 m/s. Calculate (i) the maximum height to which it rises, (ii) the total time it takes to return to the surface of the earth.
Ans: Given, the initial velocity of ball is u = 49 m/s
The final velocity of the ball at the maximum height is v = 0 m/s
Let g = 9.8 m/s2
We know that, 2as = v2- u2
Acceleration due to gravity is g and height would be H.
So replacing the above value we get 2gH = v2- u2
2 x (-9.8) x H = 0 – (49)2
-19.6 H = -2401
H = -2401/-19.6
H = 122.5 m
Now, using formula v = u + gt
=> 0 = 49 + (-9.8) x t
=> -49 = -9.8t
=> t = -9.8/-49
=> t = 5 second
Hence, the maximum height the ball reaches is 122.5 m
And the time taken by it is 5 second.
14. A stone is released from the top of a tower of height 19.6 m. Calculate its final velocity just before touching the ground.
Ans: Initial velocity u = 0 m/s
Height s = 19.6 m
Using third equation of motion
V2 = u2 + 2gs
=> V2 = (0)2 + 2 x 9.8 x 19.6
=> V2 = 384.16
=> V = 19.6 m/s
Hence, the velocity of stone just before touching the ground is 19.6 m/s.
15. A stone is thrown vertically upward with an initial velocity of 40 m/s. Taking g = 10 m/s2 , find the maximum height reached by the stone. What is the net displacement and the total distance covered by the stone?
Ans: Given, initial velocity u = 40 m/s
And g = 10 m/s2
Using the third equation of motion
v2- u2 = 2gs
=> (0)2 – (40)2 = -2 x 10 x s
=> - 160 = -20 x s
=> -160 / -20 = s
=> s = 80 m
So, total distance would be = 2 x s
=> 2 x 80
=> 160 m
Since, initial and final position is same. Therefore, total displacement would be 0.
16. Calculate the force of gravitation between the earth and the Sun, given that the mass of the earth = 6 × 1024 kg and of the Sun = 2 × 1030 kg. The average distance between the two is 1.5 × 1011 m.
Ans: Given, mass of earth m = 6 × 1024
Mass of sun M = 2 × 1030
Distance between sun and earth r = 1.5 × 1011 m
Now force of gravitation between them F = G x M x m / r2
=> F = 6.67 x 10-11 x (6 × 1024) x (2 x 1030) / (1.5 x 1011)2
=> F = 3.557 x 1022 N
17. A stone is allowed to fall from the top of a 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. Calculate when and where the two stones will meet.
Ans: Given, the height of tower is 100m.
Downward stone:
Initial velocity u = 0 m/s
Using s = ut + ½ gt2
=> s = 0 x t + ½ x 10 x t2
=> s = 5t2
Upward stone:
Initial velocity u = 25 m/s
Using s = ut – ½ gt2
=> 100 - s = 25t – ½ x 10 x t2
=> 100 - 5t2 = 25t – 5t2
=> 100 = 25t
=> t = 100/25
=> t = 4 s
So, both the stones will meet after 4 seconds.
Now, distance s = 5 x t2
=> s = 5 x (4)2
=> s = 5 x 16
=> s = 80m
Hence, the stone will meet each other at a distance of 80m.
18. A ball thrown up vertically returns to the thrower after 6s. Find (a) the velocity with which it was thrown up, (b) the maximum height it reaches, and (c) its position after 4s.
Ans: Given, the ball returns to the thrower after 6s. It means that the ball reaches the maximum height after 3 seconds.
(a) using v = u + at
=> 0 = u + (-10) x 3
=> 0 = u – 30
=> u = 30 m/s
(b) using s = ut + ½ at2
=> s = 30 x 3 + ½ (-10) x (3)2
=> s = 90 + (-5) x 9
=> s = 90 – 45
=> s = 45 m
Hence, the maximum height it reaches is 45 m.
(c) using s = ut + ½ at2
=> s = 0 + ½ (10) x (1)2
=> s = 5 m
Hence, its height above ground h = 45 – 5 = 40m.
19. In what direction does the buoyant force on an object immersed in a liquid act?
Ans: The buoyant will act in the upward direction.
20. Why does a block of plastic released under water come up to the surface of water?
Ans: Since, the density of plastic is lesser than the density of water, hence, it come up to the surface of the water.
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?
Ans: Given, the mass of substance m = 50g
And Volume of substance v = 20 cm3
So, the density of substance = mass of substance/ volume of substance
= 50/20
=2.5 g cm-3
Hence, the density of substance is greater than the density of water. Therefore, the substance will sink in water.
22. 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 mass of the water displaced by this packet?
Ans: Given, the mass of packet m = 500g
And volume of packet v = 350 cm3
So, the density of substance = mass of packet / volume of packet
= 500/350
= 1.43 g cm-3
Since, the density of this packet is lower than the density of water. Therefore, it will float on water.
Now, mass of water displaced = density of water x volume of packet
= 1 x 350
= 350g