**1) How does the force of**

gravitation between two objects change when the distance between them is

reduced to half?

gravitation between two objects change when the distance between them is

reduced to half?

ANSWER:-According to Universal

Law of gravitation, the gravitational

force of attraction between any two objects of mass M and m is proportional to the

product of their masses and

inversely proportional to the square of distance between them

Law of gravitation, the gravitational

force of attraction between any two objects of mass M and m is proportional to the

product of their masses and

inversely proportional to the square of distance between them

So, force is given by

**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?

all objects in proportion to their masses. Why then, a heavy object does not

fall faster than a light object?

ANSWER:-All objects fall on

ground with constant acceleration, called acceleration due to gravity (in the

absence of air resistances). It is constant and does not depend upon the mass of an object. Hence, heavy objects

do not fall faster than light objects.

ground with constant acceleration, called acceleration due to gravity (in the

absence of air resistances). It is constant and does not depend upon the mass of an object. Hence, heavy objects

do not fall faster than light objects.

**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 ×

10 6 m).

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 ×

10 6 m).

ANSWER:-Mass of the body, m= 1 kg

Mass of the Earth, M= 6 x1024 kg

Radius of the earth, R = 6.4 x106

m

m

Now magnitude of the

gravitational force (F) between the

earth and the body can be given

as,

gravitational force (F) between the

earth and the body can be given

as,

**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?

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 tow objects attract each other with equal force but in

opposite directions. The Earth and the moon both attract each other with equal

force. Which means that the magnitude of force with which earth attracts moon is equal to

the magnitude of force with which moon attracts earth but their directions are

opposite to each other.

law of gravitation tow objects attract each other with equal force but in

opposite directions. The Earth and the moon both attract each other with equal

force. Which means that the magnitude of force with which earth attracts moon is equal to

the magnitude of force with which moon attracts earth but their directions are

opposite to each other.

**5) If the moon attracts the**

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

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

ANSWER:-The Earth and the moon

experience equal gravitational forces from each other. However, the mass of the

Earth is much larger than the

mass of the moon. Hence, it accelerates

at a rate lesser than the acceleration rate of the moon towards the Earth.

experience equal gravitational forces from each other. However, the mass of the

Earth is much larger than the

mass of the moon. Hence, it accelerates

at a rate lesser than the acceleration rate of the moon towards the Earth.

**6) What happens to the**

force between two objects, if

force between two objects, if

**(i) The mass of one**

object is doubled?

object is doubled?

**(ii) The distance**

between the objects is doubled and tripled?

between the objects is doubled and tripled?

**(iii) The masses of**

both objects are doubled?

both objects are doubled?

ANSWER : i)-

ii)The force F is inversely

proportional to the distance

between the objects. So if the

distance between two objects is

doubled then the gravitational force of attraction between them is reduced to

one fourth of its original value. Similarly f the distance between two objects

is tripled, then the gravitational force of attraction becomes one ninth of its

original value.

proportional to the distance

between the objects. So if the

distance between two objects is

doubled then the gravitational force of attraction between them is reduced to

one fourth of its original value. Similarly f the distance between two objects

is tripled, then the gravitational force of attraction becomes one ninth of its

original value.

(iii) Again from Universal law of

attraction from equation 1 force

F is directly proportional to the product of both the masses. So if both the

masses are doubled then the gravitational force of attraction becomes four

times the original value.

attraction from equation 1 force

F is directly proportional to the product of both the masses. So if both the

masses are doubled then the gravitational force of attraction becomes four

times the original value.

**7)What is the importance of universal**

law of gravitation?

law of gravitation?

ANSWER:-Universal law of Gravitation

is important because it tells

us about the force that is responsible for binding us to Earth. The motion of

moon around the earth, the motion of planets around the sun the tides formed by rising and

falling of water level in the ocean are due to the gravitational force exerted

by both sun and moon on the earth.

is important because it tells

us about the force that is responsible for binding us to Earth. The motion of

moon around the earth, the motion of planets around the sun the tides formed by rising and

falling of water level in the ocean are due to the gravitational force exerted

by both sun and moon on the earth.

**8) What is the acceleration of**

free fall?

free fall?

ANSWER:-Acceleration of free fall

is the acceleration produced when a body falls under the influence of the force

of gravitation of the earth alone. It is denoted by g and its value on the

surface of the earth is 9.8 ms-2.

is the acceleration produced when a body falls under the influence of the force

of gravitation of the earth alone. It is denoted by g and its value on the

surface of the earth is 9.8 ms-2.

**9) What do we call the**

gravitational force between the Earth and an object?

gravitational force between the Earth and an object?

ANSWER:-Gravitational force

between the earth and an object is known as the weight of the object.

between the earth and an object is known as the 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 gis

greater at the poles than at the equator].

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 gis

greater at the poles than at the equator].

ANSWER:-W= mg

Where,

m= Mass of the body

g= Acceleration due to gravity

The value of gis greater at poles

than at the equator. Therefore, gold at the equator weighs less than at the

poles. Hence, Amit’s friend will not agree with the weight of the gold bought.

than at the equator. Therefore, gold at the equator weighs less than at the

poles. Hence, Amit’s friend will not agree with the weight of the gold bought.

**11) Why will a sheet of paper**

fall slower than one that is crumpled into a ball?

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.

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 Newton’s

of a 10 kg object on the moon and on the Earth?

of the moon is only 1/6 as strong as gravitational force on the Earth. What is

the weight in Newton’s

of a 10 kg object on the moon and on the Earth?

ANSWER:-Weight of an object on

the moon = 1/6 x Weight of an object on the Earth

the moon = 1/6 x Weight of an object on the Earth

Also,

Weight = Mass x Acceleration

Acceleration due to gravity, g

= 9.8 m/s2

= 9.8 m/s2

Therefore, weight of a 10 kg

object on the Earth = 10 x 9.8 =

98 N

object on the Earth = 10 x 9.8 =

98 N

And, weight of the same object

on the moon= 1.6 x 9.8 = 16.3 N.

on the moon= 1.6 x 9.8 = 16.3 N.

**13) A ball is thrown**

vertically upwards with a velocity of 49m/s. Calculate

vertically upwards with a velocity of 49m/s. Calculate

**(i) The maximum height**

to which

it rises.

to which

it rises.

**(ii) The total time it**

takes to return to the surface of the earth.

takes to return to the surface of the earth.

ANSWER:-equation of motion under

gravity:

gravity:

v 2 – u2= 2 gs

Where,

u= Initial velocity of the ball

v = Final velocity of the ball

s = Height achieved by the ball

g= Acceleration due to gravity

At maximum height, final velocity of the ball is zero,

i.e.,

i.e.,

v = 0

u= 49 m/s

During upward motion, g= – 9.8

m s -2

Let h be the maximum height

attained by the ball.

attained by the ball.

Hence,

Let t be the time taken by the ball to reach the

height 122.5 m, then according to the equation of motion:

height 122.5 m, then according to the equation of motion:

v = u + gt

We get,

0= 49 + t x (- 9.8)

9.8t= 49

t= 49 / 9.8= 5s

But,

Time of ascent = Time of

descent

descent

Therefore, total time

taken by the ball to return = 5 +

5 = 10s

taken by the ball to return = 5 +

5 = 10s

**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.

height 19.6 m. Calculate its final velocity just before touching the

ground.

ANSWER:-According to the equation of motion under

gravity:

gravity:

v 2 − u2 = 2 gs

Where,

u = Initial velocity of the stone= 0

v = Final velocity of the stone

s = Height of the stone = 19.6m

g = Acceleration due to gravity

= 9.8 m s −2

∴ v2 − 0 2 = 2 × 9.8 × 19.6

v 2 = 2 ×

9.8 × 19.6 = (19.6) 2

9.8 × 19.6 = (19.6) 2

v = 19.6 m s − 1

**15) A stone is thrown vertically upward with an**

initial velocity of 40 m/s. Taking g = 10 m/s 2, find the maximum height

reached by the stone. What is the net displacement and the total distance

covered by the stone?

initial velocity of 40 m/s. Taking g = 10 m/s 2, find the maximum height

reached by the stone. What is the net displacement and the total distance

covered by the stone?

ANSWER:-According to the equation of motion under

gravity:

gravity:

v 2 − u2 = 2 gs

Where,

u = Initial velocity of the stone= 40m/s

v = Final velocity of the stone= 0

s = Height of the stone

g = Acceleration due to gravity= −10 m s −2

Let h be the maximum height attained by the stone.

Therefore,

0 – (40)2 = 2 x h x (-10)

h= 40 x 40 / 20 = 80 m

Therefore, total distance covered by the stone during

its upward and downward journey= 80 + 80 = 160 m

its upward and downward journey= 80 + 80 = 160 m

Net displacement of the stone 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.

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:-MSun = Mass of the Sun = 2 × 1030 kg

MEarth = Mass of the Earth = 6 ×1024 kg

R = Average distance between the Earth and the Sun =

1.5 ×1011 m

1.5 ×1011 m

From Universal law of

gravitation,

gravitation,

**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.

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:-Let t be the point at which two stones meet

and let h be their height

from the ground

and let h be their height

from the ground

**18) A ball thrown up vertically returns to the**

thrower after 6s. Find

thrower after 6s. Find

**(a) The velocity with which it was thrown up,**

**(b) The maximum height it reaches, and**

**(c) Its position after 4 s.**

ANSWER:-Acceleration due to gravity, g = −9.8 m s −2

Equation of motion, v = u + gt will give,

0 = u + (−9.8

× 3)

× 3)

u = 9.8 × 3

= 29.4 ms− 1

= 29.4 ms− 1

Hence, the ball was thrown upwards with a velocity of

29.4 m s −1.

29.4 m s −1.

(b) Let the maximum height attained by the ball be h. Initial

velocity during the upward journey, u = 29.4 m s−1

velocity during the upward journey, u = 29.4 m s−1

Final velocity, v = 0

Acceleration due to gravity, g = −9.8 m s −2

From the equation of motion, s= ut + 1/2 at 2

h= 29.4 x 3 + 1/2 x -9.8 x (3) 2 = 44.1 m

(c) Ball attains the maximum height after 3 s. After

attaining this height, it will start falling downwards.

attaining this height, it will start falling downwards.

In this case,

Initial velocity, u = 0

Position of the ball after 4 s of the throw is given by the distance travelled by it during its downward journey in 4 s − 3

s = 1 s.

Equation of motion, s= ut + ½ gt 2 will give,

s= 0 x t + 1/2 x 9.8 x 12 = 4.9m

Total height = 44.1 m

This means that the ball is 39.2 m (44.1 m −

4.9 m) above the ground after 4

seconds.

4.9 m) above the ground after 4

seconds.

**19) In what direction does the buoyant force on an**

object immersed in a liquid act?

object immersed in a liquid act?

ANSWER:-An object immersed in a liquid experiences

buoyant force in the upward direction.

buoyant force in the upward direction.

**20) Why does a block of plastic released**

under water come up to the surface of water?

under water come up to the surface of water?

ANSWER: Because of gravitational force and buoyant.

**21) The volume of 50 g of a substance is 20 cm 3. If**

the density of water is 1 g cm −3, will the substance

float or sink?

the density of water is 1 g cm −3, will the substance

float or sink?

ANSWER:-density of the substance

= Mass of the substance /Volume of the substance

= 50 / 20

= 2.5 g cm -3

The density of the substance is more than the density of water (1 g cm −3).

Hence, the substance will sink in

water.

Hence, the substance will sink in

water.

**22) The volume of a 500 g sealed packet is 350 cm 3.**

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?

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?

ANSWER:-Density of the 500 g sealed packet= Mass of the Packet /Volume of the Packet

= 500 / 350

= 1.428 g cm −3

The density of the substance is more than the density

of water (1 g cm−3) Hence, it will sink in water.

of water (1 g cm−3) Hence, it will sink in water.

The mass of water displaced by the packet is equal to

the volume of the packet, i.e., 350g.

the volume of the packet, i.e., 350g.