Chapter 10 Gravitation

By | June 24, 2018
Class 9 | Science | Chapter 10 |Gravitation| NCERT Solutions

Question Answers, Page 134

1. State the universal law of gravitation.

Answer:
This law states that every body in the universe attracts every other body with a force which is directly proportional to the product of their masses and inversely proportional to square of distance between them.

 
 gravitational law
       G m1  m2
F=—————-
              r2    
The value of Universal gravitation constant(G) has been found to be 6.67 x 10 11 Nm2kg2
           
2. Write the formula to find the magnitude of the gravitational force between the earth and an object on the surface of the earth.
Answer:
       G mE m
F=————–
              R2    
Where mE is the mass of Earth and m is the mass of an object on its surface.
R is the radius of the Earth.
G is the gravitational constant whose value is 6.67 x 10 11 N m2kg2
Page 136

1. What do you mean by free fall?

Answer:
When an object is released from a height, it falls towards the surface of Earth under the influence of gravitational force.The motion of the object is said to be free fall.

2. What do you mean by acceleration due to gravity?

Answer:
When an object falls freely towards the surface of earth from a certain height, then its velocity changes.This changing velocity produces acceleration in the object which is known as acceleration due to gravity.It is denoted by symbol g.The value of g=9.8 m/s2

Page 138

1. What are the differences between the mass of an object and its weight?

Answer:

Mass Weight
It is the measure of inertia of body. It is the measure of gravity.
It has only magnitude It has magnitude as well direction
It is the quantity of matter contained in the body. It is the force of gravity acting on body.
Its unit is kg. Its unit is Newton.

2. Why is the weight of an object on the moon 1/6 th its weight on the earth? 

Answer:
The mass of moon is 1/100 times and its radius is 1/4 times that of the earth.As a result, the gravitational attraction on the moon is about one sixth when compared to earth.Hence the weight of an object on the moon is 1/6 th its weight on the earth.

Page 141

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

Answer:
Pressure is inversely proportional to the surface area on which the force acts.Smaller is the surface area larger will be the pressure on the surface.In the case of thin straps surface area will be very small.Hence the pressure exerted on shoulders is very large. Therefore school bags should have wide Straps so that weight of bag fall over a large area of the shoulder thus producing less pressure on shoulder.Due to less pressure, it is more comfortable to carry.

2. What do you mean by buoyancy?

The upward force exerted by a liquid on an object immersed in it is known as buoyancy.

3. Why does an object float or sink when placed on the surface of water?

If the buoyant force exerted by water is less than weight of object, the object will sink in water.
If the buoyant force exerted by water is equal to the weight of object, the object will float.

Page 142

1. You find your mass to be 42 kg on a weighing machine. Is your mass more or less than 42 kg?

Answer:
When you weigh your body, an upward force acts on it.This upward force is the buoyant force.As a result, body gets pushed slightly upwards, causing the weighing machine to show a reading less than the actual value.

2. 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?

Answer:
The cotton bag is heavier than iron bar.This is because the surface area of the cotton bag is larger than the iron bar.Hence more buoyant force acts on the cotton bag than that on an iron bar.This makes cotton bag lighter than its actual value.So the weighing machine indicates a smaller mass of cotton bag than its actual mass.

Exercises Page 145

1. How does the force of gravitation between two objects change when the distance between them is reduced to half ?

Answer:
According to the universal law of gravitation, gravitational force acting between two objects is inversely proportional to the square of the distance between them i.e.

F ∝ 1/r2

F=(G m1 m2)/r2

If distance r become r/2 then the gravitational force become four times larger than the previous value.

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?

Answer:
All objects fall towards ground with constant acceleration called acceleration due to gravity.It is constant and does not depend upon the mass of an object.Hence heavy object does not fall faster than a light object.

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.

Answer:
F=mM/r2

Mass of earth, M = 6 × 1024 kg

mass of an object ,m = 1 kg

G= 6.7 x 10 11 Nm2kg2

The object is on the surface of earth = r= R= radius of earth

r=R = 6.4 × 10 m

F= 6.7 x 10 11 ×[ (6 × 1024 ) × 1 ] / (6.4 × 10 6)2

F = 9.8 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?

Answer:
According to Universal Law of gravitation, two objects attract each other with equal force , but in opposite direction.The Earth attracts the moon with an equal force with which the moon attracts the earth.

5. If the moon attracts the earth, why does the earth not move towards the moon?

Answer:
The Earth and moon experience equal gravitational forces from each other.The mass of the earth is much larger than the mass of the moon.Hence it accelerates at a rate lesser than acceleration rate of the moon towards the Earth.Therefore 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?

Answer:
F=GmM/r2

1) Force is directly proportional to the mass of the object.If the mass of the object is doubled, then the gravitational force will also get doubled.

2) Force is inversely proportional to the square of the distance between the objects.

If the distance is doubled , then the gravitational force will become one-fourth of its original value.

If the distance is tripled, then the gravitational force will become one-ninth of its original value.

3) If masses of both objects are doubled then the gravitational force will become four times its original value.

7. What is the importance of universal law of gravitation?

Answer:
The Universal law of gravitation is important because it tells about the force that is responsible for binding us to earth, motion of moon around the earth, motion of planet around the sun, formation of tides etc.

8. What is the acceleration of free fall?

Answer:
Acceleration of free fall is 9.8 m/s2  which is constant for all objects.

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 known as weight  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 g is greater at the poles than at the equator.]

Answer:
Weight of a body on the Earth =W=mg

where m is the mass of the body and g is the acceleration due to gravity .

The value of g is greater at poles than at the equator.Therefore gold at equator weighs less than at the poles.Hence Amit’s friend will not agree with weight of the gold bought.

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

Answer:
When a sheet of paper is crumbled into a ball, then its density increases.Hence resistance to its motion through the air decreases and it falls faster than the sheet of paper.

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?

Answer:
Weight of an object on moon= 1/6 × Weight of an object on the Earth

Weight = mass × acceleration

Acceleration due to gravity, g= 9.8 m/s2

Weight of 10 kg object on the Earth= 10 × 9.8 = 98 N

weight of the same object on moon = 1/6 × 98 = 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.

Answer:
v2-u2 =2gS

Initial velocity of the ball , u= 49 m/s

Final velocity of the ball ,v = 0 m/s

During upward motion= -9.8 m /s2

Let h be the maximum height attained by the bell.

(0)2 – (49)= 2 (-9.8) h

h=122.5 m

v= u + gt

0 = 49 + (-9.8) t

t= 5 s

Time of ascent = Time of descent

Total time taken by the ball to return= 10 s

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.

Answer:
According to equation of motion

v2-u2 = 2gS

Initial velocity of stone , u = 0 m/s

Final velocity of stone , v =

Height of the stone = 19.6 m

Acceleration due to gravity = 9.8 m/s2

v2 – (0)= 2 × 9.8 × 19.6

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?

Answer:
Initial velocity of stone = 40 m/s

Final velocity of stone = 0 m/s

Acceleration due to gravity ,g = -10 m/s2

let h be the maximum height attained by the stone

02 – (40)2 = 2 × (-10) × h

h= 80 m

Total distance covered by the stone during its upward and downward journey = 80 +80 =160 m

Net displacement during its upward and downward journey = 80 + (-80) = 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.

According to the Universal Law of Gravitation, the force of attraction between the Earth and Sun is given by

F= G × Msun × Mearth /R2

Msun = Mass of the Sun = 2 × 1030 kg

Mearth = Mass of Earth = 6 × 1024 kg

R= Average distance between the Earth and Sun= 1.5 × 1011 m

G = Universal gravitational constant = 6.7 × 10 -11 Nm2 Kg-2 

F=[6.7 × 10 -11× 2 × 1030 ×6 × 1024] / (1.5 × 1011)2

F= 3.57 × 1022 N

The force of gravitation between the Earth and sun is 3.57 × 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.

Answer:
When the stone dropped from tower

Initial velocity = 0 m/s

Displacement of the stone = S

Time = t

Acceleration due to gravity = 9.8 m/s2

From the equation of motion

S= ut + ½ at2

S = 0×t + ½ × 9.8 × t2

S = 4.9 t2

When the stone thrown upwards

Initial velocity = 25 m/s

Displacement of the stone = S´

Time = t

Acceleration due to gravity = -9.8 m/s2

S= ut + ½ at2

S = 25×t + ½ × (-9.8) × t2

S =25 t – 4.9 t2

After combining both the equations we get , height of tower as 100 m.

S + S’ = 100

25t -4.9t2 + 4.9t2 = 100

t= 4s

The falling stone has covered a distance (S) = 4.9 × (4)2 = 78.4 m

Therefore the stones will meet after 4 s at a height (100-78.4) =20.6 m from the ground.

18. A ball thrown up vertically returns to the thrower after 6 s. Find (a) the velocity with which it was thrown up, (b) the maximum height it reaches, and (c) its position after 4 s.

a) Time to ascent is equal to time to descent.The ball takes a total of 6 s for its upward and downward journey.

Hence , it has taken 3s to attain the maximum height.

Final velocity of the ball at the maximum height , v= 0 m/s

Acceleration due to gravity ,g = – 9.8 m/s2

v= u +at

o= u +[ (-9.8) × 3 ]

u= 29.4 m/s

The ball was thrown upward with a velocity of 29.4 m/s

b) Let the maximum height attained by the ball be h

Initial velocity during upward journey , u = 29.4 m/s

Final velocity , v = 0 m/s

Acceleration due to gravity , g = -9.8 m/s2

S = ut + ½ gt

h = 29.4 × 3 + ½ × (-9.8) × 32

h= 44.1 m

c) Ball attains the maximum height after 3 s. After attaining this height, it will start falling downwards.

Initial velocity = 0 m/s

Position of the ball after 4 s of the throw is given by the distance travelled by it during its down ward journey in 4s -3 s = 1s

Using the equation

S = ut + ½ at2

S = 0 × 1 + ½ × 9.8 × (1)2

S= 44.1 m

The height of ball above the ground after 4 s = (44.1 – 4.9) = 4.9 m

page  145

19. In what direction does the buoyant force on an object immersed in a liquid act?

Answer:
An object immersed in a liquid experiences buoyant force in upward direction.

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

Answer:
Two forces act on an object immersed in water.

1) One is the gravitational force which pulls the object downwards.

2) 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 the water.Due to this reason, a block of plastic released under water come up to the surface of 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?

Answer:
Density of substance = Mass of substance / volume of substance

Density of substance = 50/20 = 2.5 g/cm3

If  the density of an object is more than the density of a liquid, then it sinks in the liquid.

If  the density of an object is less than the density of a liquid, then it will float on the surface of liquid.

The density of the substance is more than the density of water.Hence 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 gcm–3? What will be the mass of the water displaced by this packet?

Answer:
Density of 500 g sealed packet = Mass of the packet/ Volume of the packet

= 500/ 350 = 1.428 g/cm3

The density of the substance is is more than the density of water.Hence it will sink in water.

The mass of water displaced by packet is equal to the volume of the packet i.e. 350g.

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