This page contains NCERT book Solutions class-9 Gravitation starting from page 143 at the end of the chapter. I have also been writing the notes for this chapter to learn more about notes you can follow this

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gravitation assignment(FA)**Question 1**

How does the force of 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 attrection between any two objects of mass

$M$ and $m$ is proportional to the product of their masses

and inversly proportional to the square of distance $r$ between them

So, force $F$ is given by

$F = G\frac{{M \times m}}{{{r^2}}}$

Now when the distance $r$ is reduced to half then force between two masses becomes

$F’=G\frac{M\times m}{\left ( \frac{r}{2} \right )^2}$

or,

$F’=4F$

Clearly , if distance between two objects is reduced to half then the gravitational force becomes four times larger than its previous value.

**Question 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**

Weight of any object of mass $m$ on the surface of earth is ,

$W=mg$

where $g$ is the acceleration due to gravity.

Now from Universal Law of gravitation , force acting on any object due o gravitational pull of eart is

$F = G\frac{{M \times m}}{{{R^2}}}$

where $M$ is the mass of the earth and $R$ is the radius of the earth

Now,

Weight of object on surface of earth is equal to gravitatinal force acting on it.

So,

\(mg = G\frac{{M \times m}}{{{R^2}}}\)

Rearranging above equation we get

\(g = G\frac{M}{{{R^2}}}\)

From this expression for acceleration due to gravity $g$ it is clear that $g$ does not depend on the mass of the objects. It is constant and is same for both heavy and light masses.

Hence heavy objects do not fall faster then light objects

**Question 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 $6 \times 10^{24} kg$ and radius of the earth is $6.4 \times 10^{6} m$.)

**Answer**

From Universal law of gravitation , force exerted on an object of mass $m$ by earth is given by

$F = G\frac{{M \times m}}{{{R^2}}}$ (1)

where,

Mass of earth, $M=6 \times 10^{24}Kg$

Mass of the object, $m=1Kg$

Gravitational constant $G=6.7 \times 10^{-11}Nm^{2}Kg^{-2}$

Here radius of rart $R$ is the distance between the objects as object under consideration is on the urface of earth. So,

$R=6.4 /times 10^{6}m$

Putting all these values in equation 1 we get

\(F = \frac{{6.7 \times {{10}^{ – 11}} \times 6 \times {{10}^{24}} \times 1}}{{{{\left( {6.4 \times {{10}^6}} \right)}^2}}} = 9.8N\)

**Question 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 tow objects attract each other with equal force but in opposite directions. The Earth and the moon both attracts 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,

**Question 5**

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

**Answer**

Earth and the moon both exerts equal gravitational force on each other. The earth does not moves towards moon as a result of this force of atraction because the mass of earth is much larger then that of moon due to which acceleration experienced by earth due to gravitational pull of moon is very small in comparison to that experienced by moon due to earth. This is the reason earth does not moves towards moon.

**Question 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**

From Universal law of gravitation , force exerted on an object of mass $m$ by earth is given by

$F = G\frac{{M \times m}}{{{R^2}}}$ (1)

(i) When mass of the object say $m$ is doubled than

$F’ = G\frac{{M \times 2m}}{{{R^2}}}=2F$

So as the mass of any one of the object is doubled the force is also doubled

(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.

(iii) Again fron 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.

**Question 7**

What is the importance of universal law of gravitation?

**Answer**

Universal law of Gravitation is important because it 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.

**Question 8**

What is the acceleration of free fall?

**Answer**

When objects falls towards the Earth from a certain height it falls freely towards the earth under the effect of gravitational force alone. So acceleration of free fall is the acceleration experienced by any object when it falls freely under the influence of gravitational force alone.

It is denoted by $g$ and its value on the surface of earth is $9.8ms^{-2}$.

**Question 9**

What do we call the gravitational force between the earth and an object?

**Answer**

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

**Question 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**

The value of acceleration due to gravity varies at different places on the earth . It decreases from poles to equator.

Now, Weight of body on earth is given by

$W=mg$

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

Since the value of $g$ is greater at poles then it is at equator. This is the reason that weight of gold on equator is less than the weight of gold on poles. Hence, Amit’s friend will not agree with the weight of the gold bought.

**Question 11**

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

**Answer**

When we crumble a sheet of paper into a ball then its surface area becomes much lesser than the surface area of a plain flat sheet of paper. The plain sheet of paper experience more resistance due to air than the crumpled ball and it will fall slower than the crumpled ball even if they both experience same force of gravity.

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