gravitation notes

7/26/2019 Gravitation Notes

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Class 9 - Science - Ch10 – Gravitation

What is centripetal force

Answer: Any motion in a curved path represents accelerated motion, and requires a force directed

toward the center of curvature of the path. This force is called the centripetal force .

Q1. State the universal law of gravitation.

Answer: Every object of the universe attracts other object. The force of attraction between the

two objects is proportional to the product of their mass and inversely proportional to the

square of the distance between them. The direction of this force is along the line joining the

centres of the objects.

If m1 and m2 are the two objects separated by a distance d , then force attraction between them

is:

F = Gm1m2/d2

where G is the universal Gravitation constant = 6.67 × 10-11 Nm2/kg2

Q2: What is the importance of Universal Law of Gravitation? (or)

State any one phenomena related to the Universal Law of Gravitation.

Answer: The law is universal i.e. it is applicable to all bodies, whether the bodies are big or

small, whether they are celestial or terrestrial. It successfully explains various phenomena:

1. the force that binds us to the earth.

2. the motion of the moon around the earth

3. the motion of planets around the Sun

4. the tides due to the moon and the Sun.

5. it also helps us finding the masses of planets and stars.

Q3 Why is G called the Universal Constant?

Answer: At any place in the universe and at any time, the value of G is found to be constant

for any two bodies. Thus G is called the universal constant of gravitation.

It is defined as force of attraction acting between two objects of mass 1 kg each placed at a

distance of 1 m.

Mathematically, G = F.d2/m1m2

Thus the SI unit of the universal constant of gravitation is Nm2/kg2.

The value of G is 6.67 × 10-11 Nm2/kg2



Q: Who measured the value of G first time, experimentally?

Answer: Henr

Q: What is the gravitational force between the Earth and a body called? In which

direction does it occur?

Answer: Weight of the body or gravity. It always acts towards the centre of the earth i.e.

vertically downwards.

Q: An object moves in a circular motion due to centripetal force, acting towards the

center. The moon also rotates around the earth? Does centripetal force acts on it? Why

does the moon not fall on the earth?

(or)

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

Answer: Yes the centripetal force acts on the moon. This force is due to gravitational force

between the earth and the moon and it acts on both the objects. Gravitational force is always

attractive, still the moon does not fall on the earth, because the tangential speed (due to

centripetal force) of the moon make it escape from the gravitational force and is enough to

hold it in its orbital path.

Q: 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: The two objects attract each other with equal forces of attraction but in opposite

directions.

Q: How gravitational force is different from or similar to magnetic force (between two

magnets) or coulomb force (between two charged object)? Answer: Similarity: These three forces follow inverse square rule i.e. force between the two

objects is inversely proportional to the square of distance between them.

Difference: While gravitational force is always attractive, magnetic force and coulomb forces

can be attractive or repulsive (e.g. North-North pole repel each other.). Among the three,

gravitational force is the weakest.

Q: 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.

Answer: Given, mass of the earth (mE) = 6 × 1024 kg

mass of the sun (mS) = 2 × 1030 kg

Distance between the bodies (d) = 1.5 × 1011m

Gravitational Constant (G) = 6.67 × 10-11 Nm2/kg2

Applying formula of Newton's Law of Gravitation,



F = GmEmS/d2 = 6.67 × 10-11 × 6 × 1024 × 2 × 1030 / (1.5 × 1011)2

F = 80.04 × 10-11+24+30/ 2.25 × 1022 = 35.57 × 1043-22 = 35.57 × 1021

F = 3.56 × 1022

N

Q: The Earth attracts an apple. Does the apple also attract the Earth? If it does, why

does the Earth not move towards the apple?

Answer: According to Newton's law of gravitation, both apple and the earth attract each otherwith equal force but in opposite directions. Also they they produce different accelerations

depending on the mass of the object. It means apple also attract the Earth. Since the mass of

the earth is extremely large as compared to mass of the apple, acceleration of the earth due to

this force of attraction is very low (of order 10-25 m/s2).

Mathematically, mass of an apple (mapple) = 150g = 0.15 kg

mass of the earth (mE) = 6 × 1024 kg

acceleration acting on apple due to gravity (g) of earth = 9.8 m/s2

Weight of the apple = mapple× g = 0.15 × 9.8 = 1.47 N

⇒ Earth also experiences 1.47 N force.

i.e. mE × a = 1.47Na = 1.47 / 6 × 1024= 2.45 × 10-25 m/s2 (extremely small value)

Q: How is gravitational force of attraction between two bodies affected if

(i) Mass of both bodies is doubled.

(ii) Distance between them is halved.

Answer: The gravitational force between two objects is directly proportional to the product of

their mass and inversely proportional to the square of the distance between them.

(i) if mass of both bodies is doubled, the force of the attraction will increase by 4 time.

(ii) if distance between them is halved, the force of attraction will increase by 4 times.

In case above two cases occur in parallel, the force of attraction will increase by 16 times.

Q: 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: The gravitational force between two objects is directly proportional to the product

of their mass and inversely proportional to the square of the distance between them.

F = Gm1m2/d2

http://3.bp.blogspot.com/-mdFx6z4w9No/UDjHq1A6AOI/AAAAAAAABeM/yxoJH36D8vk/s1600/cl9SciCh10Fig3.jpg



(i) Doubled

If m1 becomes 2m1

F New = G2m1m2/d2 = 2(Gm1m2/d

2) = 2F

(ii) One fourth and one-ninthif distance between objects is doubled i.e. 2d, F New = Gm1m2/(2d)2 = Gm1m2/4d2

F New = F/4

if distance is tripled i.e. 3d, F New = Gm1m2/(3d)2 = Gm1m2/9d2

F New = F/9

(iii) four times

If both masses are doubled i,e, 2m1 and 2m2

F New = G2m12m2/d2 = 4(Gm1m2/d

2) = 4F

Q: An object is placed at the surface of the earth and is at distance R from the center ofthe earth. The object weighs 180N. What will be its weight if it is at distance 3R from

the center of the earth.

Answer: 20N.

Q: Does the force of attraction between two objects depend on the properties of

intervening medium?

Answer: No.

Q: Does Law of gravitation obey Newton's third law of motion?

Answer: Yes.

Q: What is free fall?

Answer: The falling of a body from a height towards the earth under the influence of

gravitational force of the earth alone is called free fall.

Q: Define 'g' or acceleration due to gravity? Does it depend on the mass of the body(near the surface of the earth)experiencing 'g'?

Answer: The constant acceleration experienced by a freely falling object towards the earth is

called acceleration due to gravity (g). Its average value on the surface of the earth is 9.8 m/s2.

It does not depend on the mass of the body experiencing 'g'.

i.e. g = GmE/R 2 = 9.8 m/s2.

where mE is the mass of the earth, R is the radius of the earth and G is the universal constant.

Q: (a) What is the relationship between g and G?

(b) Show mathematically whether g (acceleration due to gravity on the earth) depends

on the mass of the object itself or not. (c) Show that for a given location on the surface of the earth g is almost constant.



Answer: Let ME is the mass of the earth,

m is the mass of the object on the surface of the earth.

R is the radius of the earth

g is the acceleration due to gravity and

G is the universal constant.

According to Newton's second law, Force on the body due to acceleration due to gravity is

F = mass(m) × acceleration due to gravity(g) = m×g ...(I)

Using Newton's law of gravitation, the force of attraction F = GmME/R 2 ... (II)

Since both these forces are equal, equating I and II,

mg = GmME/R 2

⇒ g = GME/R 2 ...(III)

The above equation (III) shows, acceleration due to gravity(g) is independent of its mass. It

depends on the mass of the earth(or planet) and the distance between the two objects.

For a given location on the surface of the earth, ME and R are constant.

∴ for that location value of g is constant.

Q: Why is the weight of an object on the moon 1/6th its weight on the earth? or

Show that the weight of an object on moon is 1/6th

its weight on earth Answer:

Let 'm' be the mass of an object.

R E be radius of the earth = 6400km = 6.4 × 106 m

ME = mass of the earth = 5.98 × 1024 kg

R M = radius of the moon. = 1.74 × 106 m

MM = mass of the moon = 7.36 × 1022 kg

WE = weight of an object on the earth.

WM = weight of an object on the moon.Using Newton's Law of gravitation,

WE = GMEm/R E2

WM = GMMm/R M2

⇒ WM/WE = MM/R M2 × R E

2/ME = MMR E2 /MER M

2

⇒ WM/WE = (7.36 × 1022)(6.4 × 106)2 /(5.98 × 1024)(1.74 × 106)2

⇒ WM/WE = 0.165 = 1/6

⇒ WM = WE/6

Q: 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 under the influence of gravity and experience constant acceleration

(g).

g = GME/R 2

Since g is constant for a location and independent of mass of the object, heavy objects do notfall faster than light objects.

Q: 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: Given,

R E radius of the earth = 6.4 × 106 m

ME = mass of the earth = 6 × 1024 kg

G = Universal Gravitational Constant = 6.67 × 10-11 Nm2/kg2 m = mass of object = 1kg

According to Newton's Law of gravitation, the gravitation force (F) is

F = GMEm/R E2

F = (6.67 × 10-11)(6 × 1024)(1)/(6.4 × 106)2

F = 9.8N

Q: Define mass.

Answer: The mass of the body is the quantity of matter it contains. It is the measure of inertia

of the

body. It is a scalar quantity. Its SI unit is kg. The mass of an object is constant and does not

change from place to place.

Q: Define weight? How it is related to mass?

Answer: The weight of the body is the force experienced by the body due to its gravity. It is a

vector quantity and always directs towards the centre of the earth. The SI unit of weight is

Newton (N).

Weight is also called force of gravity on the body.

Weight and mass are related as follows:

Weight = mass(m) × acceleration due to gravity(g) = mg

Q: Mass of an object is 10 kg. What is its weight on the Earth? (g = 9.8 m/s2.)

Answer: Weight = mass(m) × acceleration due to gravity(g) = mg

W = 10 × 9.8 = 98N

Q: What are the differences between the mass of an object and its weight?



Answer:

Mass Weight

1. It is the quantity of the matter

contained in the body.

1. It is the gravitational force of attraction on the

body by the earth(planet).

2. SI unit is kg 2. SI unit is Newton(N)

3. It is a scalar quantity i.e. has

magnitude only.

3. It is a vector quantity i.e. has both magnitude

and direction. e.g. On the Earth, its direction is

always towards the centre of the earth/planet.

4. It is a measure of inertia of the body. 4. It is the measure of the gravity.

5. It is measured by physical or beam

balance.

5. It is measured by spring balance calibrated to

read in Newton scale or Kg-Wt.

6 . It is constant for a body and does not

change from place to place.

6 . It is not constant but varies as the value of

gravity changes place to place.

.

Q: Gravitational force on the surface of the moon is only 1/6th 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? What is the value of 'g' at the surface of the moon?

Answer: weight = mass × acceleration = mg

Given mass of the object (m) = 10kg

Value of g on the earth = 9.8 m/s2.

Weight of the object on the earth (WE) = 10 × 9.8 = 98N.

Weight of the object on the moon (WM) = 1/6th of WE = 98/6 = 16.34 N

Acceleration due to gravity at the moon's surface = WM /m = 16.34 / 10 = 1.63 m/s2.

Q: Is acceleration due to gravity a vector or a scalar? Write its S.I. unit.

Answer: It is a vector quantity and hence has both magnitude and direction. The SI unit is

m/s2.

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