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Gravitation NCERT Solutions - Science & Technology for UPSC CSE

Page No. 102

Q1. State the universal law of gravitation.
Ans: Everybody in this universe attracts every other body with a force, which is directly proportional to the product of their masses and inversely proportional to the square of distance between their centres.

Universal Law of GravitationUniversal Law of Gravitation


Q2. Write the formula to find the magnitude of the gravitational force between the earth and an object on the surface of the earth.
Ans: Consider F as the force of attraction between an object on the surface of earth and the earth.
Let mass of earth = M
Mass of object = m.
If radius of the object is comparatively negligible, r ≈ radius of earth = R
F = GMm/R2

Page No. 104


Q1. What do you mean by free fall?
Ans: When an object falls with a constant acceleration, under the influence of force of gravitation of the earth, object is said to have free fall.

Q2. What do you mean by acceleration due to gravity?
Ans: During the course of its free fall, a body accelerates due to the force of gravity acting on it. This acceleration is known as acceleration due to gravity.


Page No. 106


Q1. What are the differences between the mass of an object and its weight?
Ans:

Gravitation NCERT Solutions | Science & Technology for UPSC CSE


Q2. Why is the weight of an object on the moon 1/6th its weight on the earth?
Ans: 
Mass of the moon (M) = 7.4 × 1022 kg
Radius of the moon (R) = 1.74 × 106 m
Gravitational constant (G) = 6.7 × 1011 Nm2kg2
We know that acceleration due to gravity(g) = GM/R2
Also, weight , W = mg
W = GMm/R2
Let the mass of the object be m, Let's its weight of moon be Mand its radius be Rm
By applying the universal law of gravitation, the weight of the object on the moon will be:Gravitation NCERT Solutions | Science & Technology for UPSC CSE  (1)
Let the weight of the same object on the earth be We. The mass of earth is M and its radius is R.
Gravitation NCERT Solutions | Science & Technology for UPSC CSE (2)
Substituting the values in equations (1) and (2) we get:
Wm= 2.431 x 1010G x m
and We = 1.474 x 1011 G x m
On dividing Wm and We we get:
Gravitation NCERT Solutions | Science & Technology for UPSC CSE
∴ Weight of the object on the moon = Gravitation NCERT Solutions | Science & Technology for UPSC CSEits weight on earth


Page No. 109


Q1. Why is it difficult to hold a school bag having a strap made of a thin and strong string?
Ans:

  • It is difficult to hold a school bag having a thin strap because the pressure on the shoulders is quite large. 
  • This is because the pressure is inversely proportional to the surface area on which the force acts. 
  • The smaller is the surface area; the larger will be the pressure on the surface. In the case of a thin strap, the contact surface area is very small. Hence, the pressure exerted on the shoulder is very large.


Q2. What do you mean by buoyancy? 
Ans: 

  • The upward force exerted by a liquid on an object immersed in it is known as buoyancy.
    Gravitation NCERT Solutions | Science & Technology for UPSC CSE
  • When you try to immerse an object in water, then you can feel an upward force exerted on the object, which increases as you push the object deeper into water.


Q3. 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 liquid, then it sinks in the liquid.
    Gravitation NCERT Solutions | Science & Technology for UPSC CSE
  • This is because the buoyant force acting on the object is less than the force of gravity. 
  • On the other hand, if the density of the object is less than the density of the liquid, then it floats on the surface of the liquid. 
  • This is because the buoyant force acting on the object is greater than the force of gravity. 


Page No. 110


Q1. You find your mass to be 42 kg on a weighing machine. Is your mass more or less than 42 kg? 
Ans: Mass is always a constant quantity. Therefore, it cannot be more or less than 42 kg.

Q2. 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: The correct answer is cotton bag is heavier than iron bar.
The reason is:

True weight = (apparent weight + up thrust)

  • The density of cotton bag is less than that of the iron bar, so the volume of cotton bag is more compared to iron bar. So the cotton bag experience more upthrust due to the presence of air.
  • Therefore in the presence of air, the true weight of cotton bag is more compared to the true weight of iron bar.


Page No. 111


Q1. How does the force of gravitation between two objects change when the distance between them is reduced to half?
Ans: 
The force of gravitation between two objects of masses m1 and m2 at separation r is given by:
F = (G m1m2)/r2
When the distance between them is reduced to half, the gravitational force.
F' = (G m1m2)/r2
= (G m1m2)/ (r/2)2
= (4 G m1m2)/(r2) = 4F
The gravitational force becomes four times.

Q2. 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:
The acceleration due to gravity of a freely falling body is independent of the mass of falling body. Thus, both heavy and light object fall with same acceleration.

Q3. 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:
Here, mass of the earth, M = 6 x 1024 kg
Mass of the object, m = 1 kg, radius of the earth, R = 6.4 x 10m, G = 6.7 x 10-11 Nm2kg-2 
The magnitude of gravitational force between the earth and object is given by:
Force of gravitation between them,Gravitation NCERT Solutions | Science & Technology for UPSC CSE
Gravitation NCERT Solutions | Science & Technology for UPSC CSE 

Q4. 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 force or the same as the force with which the moon attracts the earth? Why?
Ans: 

  • Earth attracts the moon with an equal and opposite force as moon attracts the earth. 
  • This is in accordance with Newton’s law of gravitation according to which gravitational force is the mutual force of attraction which is also equal as per to the third law of motion.

Q5. If the moon attracts the earth, why does the earth not move towards the moon? 
Ans:

  • The moon revolves around the earth because gravitation force of earth on moon provides the necessary centripetal force for circular motion.
  • The moon also attracts the earth, due to which earth also revolves around the moon in circular orbit, but due to very large mass of earth, the motion of earth is not observed.
  • It may be kept in mind that there is no linear motion of earth towards moon or moon towards earth. The gravitational force between them keeps on changing the direction of motion of moon or earth in circular orbit.

Q6. What happens to the force between two objects, if 
(a) the mass of one object is doubled? 
(b) the distance between the objects is doubled and tripled? 
(c) the masses of both objects are doubled? 
Ans: Let masses = m1 and m2, distance between masses = r.
According to universal law of gravitation F ∝ m1m2 and F ∝ 1/r2.
(a) If one mass, say m1 is doubled, and F ∝ m1,  then F gets doubled.
(b) If distance is doubled and F ∝ 1/r2, force becomes one-fourth, i.e. 1/(2)2.
If distance is tripled and F ∝ 1/r2, force becomes one-ninth, i.e. 1/(3)2.
(c) If both masses are doubled and F ∝ m1m2, force becomes 4 times, i.e. (2m1)(2m2) = 4m1m2 

Q7. What is the importance of universal law of gravitation? 
Ans: Universal law of gravitation has successfully explained the phenomena which were earlier considered to be separate:
(a) It explains about the force which holds us on earth.
(b) It explains the motion of planets around the sun.
(c) It explains the motion of moon around the earth.
(d) It explains about occurrence of tides in the ocean.

Q8. What is the acceleration of free fall?
Ans: When a body falls freely and accelerates at every point of its motion due to gravitational force alone. This is called acceleration of free fall. This acceleration is known as the acceleration due to gravity on the earth’s surface. It’s denoted by ‘g’ and its value is 9.8m/s2 and it’s constant for all objects close to earth’s surface (irrespective of their masses).

Q9. What do we call the gravitational force between the earth and an object? 
Ans: Gravity is the name of the gravitational force between earth and the object.

Q10. 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: Earth is not a perfect sphere. It is flattened at the poles. Thus, the value of ‘g’ is greater at poles than at equator (as g ∝ 1/r2).  This means weight of gold bought at poles becomes lesser at equator and the friend does not agree with the weight.

Q:11. Why will a sheet of paper fall slower than one that is crumpled into a ball?
Ans:
 

  • Sheet crumpled into a ball has a small surface area as compared to that of an unfolded sheet. Therefore, the unfolded sheet will experience more friction due to air as compared to the crumpled ball in spite of the same force of gravity acting upon them.
  • The larger friction of air slows down the unfolded sheet so it will fall slower than the sheet crumpled into a ball.

Q12. 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: Here, mass of object, m = 10 kg, g on the earth’s surface = 9.8 ms-2 
Weight of the object on the earth’s surface = mg
= 10 kg x 9.8 ms-2
= 98.0 kg ms-2 = 98 N
The weight of object on moon is 1/6th that of object on earth, so the weight of the object on the moon:
= 1/6 x 98 N= 16.34 N.

Page No. 112

Q13. A ball is thrown vertically upwards with a velocity of 49 m/s. Calculate 
(a) the maximum height to which it rises.
(b) the total time it takes to return to the surface of the earth. 
Ans: 
(a) Initial velocity, u = 49 ms-1, Final velocity, v = 0
Maximum height, H = ?
Acceleration due to gravity, g = + 9.8 ms-2 (downward)

Gravitation NCERT Solutions | Science & Technology for UPSC CSEAs object is moving upward, so a = -gFrom relation  v2 = u+ 2as , we have a = -g , s = H
 v= u- 2gH
Gravitation NCERT Solutions | Science & Technology for UPSC CSE
Gravitation NCERT Solutions | Science & Technology for UPSC CSE
⇒ H = 122.5 m
(b) When ball returns on the surface of earth, displacement, s = 0
∴ Relation, s = ut + Gravitation NCERT Solutions | Science & Technology for UPSC CSEat2 gives s = ut -Gravitation NCERT Solutions | Science & Technology for UPSC CSEgt2
0 = (49 ms-1) t -Gravitation NCERT Solutions | Science & Technology for UPSC CSEx 9.8 t2
⇒ t (49 -4.9 t) = 0
t = 0 or 49 - 4.9 t = 0 ⇒ t =Gravitation NCERT Solutions | Science & Technology for UPSC CSE
As t ≠ 0, so t = 10s
The maximum height is 122.5 m and total time is 10 s.

Q14. 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, height, h = 19.6 m and g = 9.8 ms-2
Final velocity,Gravitation NCERT Solutions | Science & Technology for UPSC CSE
Gravitation NCERT Solutions | Science & Technology for UPSC CSE
= 19.6 ms-1.

Q15. 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 are the net displacement and the total distance covered by the stone?
Ans: Initial velocity, u = 40 ms-1
g = -10 ms-2 (upward motion)
Final velocity, v = 0
During upward motion, g = -10 ms-2
Gravitation NCERT Solutions | Science & Technology for UPSC CSE
Net displacement on returning back = zero
Total distance = 80 m + 80 m = 160 m

Q16. 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: Mass of earth, Me = 6 x 1024 kg
Mass of sun Ms = 2 x 1030 kg and
Distance, r = 1.5 x 1011 m
Gravitational constant, G = 6.67 x 10-11 Nm2/kg2
Force, Gravitation NCERT Solutions | Science & Technology for UPSC CSE
Gravitation NCERT Solutions | Science & Technology for UPSC CSE
= 3.56 x 1022 N

Q17. 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:  u1 = 0
Let the stones meet at a height h above the ground. Stone 1 covers a distance (100 - h); g = 10 m/s2.
(100 - h) = 0 + Gravitation NCERT Solutions | Science & Technology for UPSC CSE
⇒ 100 - h = 5 t2 ...(i)
u2 = 25 m/s
Stone 2 covers a distance h
g = - 10m/s2
h = u2t - Gravitation NCERT Solutions | Science & Technology for UPSC CSE
⇒ h = 25 t - 5 t2 ...(ii)
From (i) and (ii), we get 
100 - 25 t + 5 t2 = 5 t2 
100 - 25 t = 0
or t = 4 s (Stones meet 4 s after they are thrown)
h = 25(4) - 5(4)= 100 - 80 = 20 m above the ground.

Q18. 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.
(c) its position after 4s.
Ans:
 

Time of ascend = Time of descending

⇒  Time taken to reach the top, t = 3 s.
⇒  Final velocity, v = 0, g = -9.8 ms-2.
(a) Initial velocity, u = v - gt = 0 - (-9.8) (3)
= 29.4 ms-1
(b) Maximum height reached, h = (v2 - u2)/g = (29.4)2/(2 x 9.8)
= 44.1 m
(c) After 4s, ball has started falling and has fallen by some distance h' for 1s.
Here, initial velocity u' = 0, t = 1s
g = + 9.8 ms-1
h' = u't + Gravitation NCERT Solutions | Science & Technology for UPSC CSE = 0  + Gravitation NCERT Solutions | Science & Technology for UPSC CSE
The ball is at a height, (44.1 - 4.9) = 39.2 m above the ground.

Q19. In what direction does the buoyant force on an object immersed in a liquid act?
Ans: An object immersed in a liquid experiences buoyant force in the upward direction.

Q20. Why does a block of plastic released under water come up to the surface of water?
Ans:

  • Two forces act on an object immersed in water. One is the gravitational force, which pulls the object downwards, and the other is the buoyant force, which pushes the object upwards. 
  • If the upward buoyant force is greater than the downward gravitational force, then the object comes up to the surface of the water as soon as it is released within water. 
  • Due to this reason, a block of plastic released under water comes up to the surface of the water.

Q21. The volume of 50g of a substance is 20 cm3. If the density of water is 1g cm-3, will the substance float or sink?
Ans: 

  • If the density of an object is more than the density of a liquid, then it sinks in the liquid. On the other hand, if the density of an object is less than the density of a liquid, then it floats on the surface of the liquid.
  • Here, density of the substance = Gravitation NCERT Solutions | Science & Technology for UPSC CSE
  • The density of the substance is more than the density of water (1 g cm−3). Hence, the substance will sink in water.

Q22. 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:

  • Density of the 500 g sealed packetGravitation NCERT Solutions | Science & Technology for UPSC CSE
  • The density of the substance is more than the density of water (Gravitation NCERT Solutions | Science & Technology for UPSC CSE). Hence, it will sink in water.
  • The mass of water displaced by the packet is equal to the volume of the packet, i.e., 350 g.

The document Gravitation NCERT Solutions | Science & Technology for UPSC CSE is a part of the UPSC Course Science & Technology for UPSC CSE.
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FAQs on Gravitation NCERT Solutions - Science & Technology for UPSC CSE

1. What is gravitational force?
Ans. Gravitational force is the force of attraction between any two objects in the universe. It is a fundamental force that governs the motion of planets, stars, and galaxies. The magnitude of gravitational force depends on the masses of the objects and the distance between them. The force is always attractive and acts along the line joining the centers of the objects.
2. What is the law of gravitation?
Ans. The law of gravitation states that every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This law was first proposed by Sir Isaac Newton in 1687 and is one of the most important laws in physics.
3. How does the mass of an object affect its gravitational force?
Ans. The mass of an object directly affects its gravitational force. The greater the mass of an object, the greater its gravitational force. For example, the gravitational force between the Earth and the Sun is much greater than the force between the Earth and the Moon, because the Sun has a much greater mass than the Moon.
4. Why do objects fall towards the Earth?
Ans. Objects fall towards the Earth because of the gravitational force between the Earth and the object. The Earth's mass is so large that it exerts a strong gravitational force on all objects near its surface. This force pulls objects towards the center of the Earth and is responsible for the phenomenon of gravity.
5. How does the distance between two objects affect their gravitational force?
Ans. The distance between two objects inversely affects their gravitational force. The greater the distance between two objects, the weaker their gravitational force. This is because the force of gravity is spread out over a larger area as the distance between the objects increases. For example, the force of gravity between the Earth and the Moon is weaker than the force between the Earth and the Sun, because the Moon is much closer to the Earth than the Sun.
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