Force

1 mark questions

1. What is ‘gravity’?
Ans: Gravity is the gravitational force of attraction between the planet or a satellite with an object on or near to the surface of the the planet or a satellite. 

2. What is ‘gravitation’?
Ans: The mutual of attraction between any two bodies in the universe is called gravitation or force of gravitation.
3. State Newton’s law of gravitation.
Ans: Newton's law of gravitation states that "The gravitational force between two bodies is directly proportional to the product of their masses and inversely proportional to the square of distance between their centers."
4. Define the universal gravitational constant G.
Ans: The force of attraction between two bodies of unit masses which are separated by unit distance apart from their center is called gravitational constant. It is denoted by letter G. Its value is 6.67×10-11 Nm²Kg^-2.
5. Give the SI unit and value of gravitational Constant G.
Ans: The SI unit of gravitational constant G is Nm²Kg^-2. It value is 6.67×10-11.
6. What do you understand by the term “acceleration due to gravity?”
Ans. The acceleration produced on a falling body due to gravity is called acceleration due to gravity. It is denoted by letter 'g'.
7. Give the mathematical equation for Newton’s law of gravitation.
Ans: F=(Gm₁m₂)/d²

8. Why can one Jump higher on the surface of the moon?
Ans: We can jump higher on the surface of the moon because acceleration due to gravity on moon is less than that on earth. The value of acceleration due to gravity on moon is 1.6 m/s². In other words we are pulled downwards with less force on the moon.
9. What is the weight of a body at the center of the earth? Why?
Ans: The weight of a body at the center of the earth is zero Newton because the value of acceleration due to gravity at the center of the earth is zero.
10. What is a gravitational field?
Ans: The region or space surrounding a body in which another body feels the force of gravitational force of attraction is called gravitational field.
11. What is gravitational force?
Ans: The force of attraction between two bodies in the universe is called gravitational force.
12. What are the factors that affect the gravitational force?
Ans: The factors that affect the gravitational force are masses of the objects and distance between their centers.
13. What do you mean by acceleration due to gravity is 9.8 m/s²?
Ans: Acceleration due to gravity is 9.8 m/s² means the velocity of the object increases by 9.8m/s every second.
14. Why does it mean by Newton's law of gravitation called as universal law?
Ans: Newton's law of gravitation is called universal law because it can be applied for both microscopic to macroscopic object and it is accepted all over the world.
15. What is null point?
Ans: Null point is the point in the space where the net effect of gravity between two or more heavenly bodies is zero.
16. Write two applications of Newton's Universal law of Gravitation.
Ans: The two applications of Newtons's Universal law of Gravitation are:
1. It is used to calculate the force or pull of gravity of the planet in universe.
2. It is also used in calculation of the trajectory of astronomical bodies and to predict there motion.

17.What is the value of one kg weight in Newton?
Ans: The value of one kg weight is 9.8N.

2 marks questions 

1. Does the value of ‘g’ depend upon the mass of body? If not, why?
Ans: The value of 'g' does not depend upon the mass of the body but it depends upon the mass of the planet in which the object is situated. According to Newton's coin and feature experiment planet or satellite exerts same force of attraction to every object whether it is heavy or light in the absence of air resistance. So, both heavy and light objects are pulled towards the center of the planet in the absence of any resistance.
2. What is the main conclusion of ‘guinea and feather experiment’?

Ans: The main conclusion of 'guinea and feather experiment' is that acceleration due to gravity is independent of mass of the the falling objects in the absence of air resistance. It means both heavy and light objects are pulled towards the center of the planet in the absence of any resistance.
3. What are the main differences between ‘g’ and ‘G’?

Ans:Differences between Acceleration due to gravity (g) and Gravitational constant (G):

S.no	Acceleration due to gravity (g)	Gravitational constant (G)
1	It is acceleration produced on a freely falling body due to gravity.	It is the mutual force of attraction between two bodies with unit mass kept at 1m distance.
2	It is vector quantity.	It is scalar quantity.
3	It differs from place to place.	It remains constant everywhere.
4	It unit is m/s2	Its unit is Nm2/Kg2.

4. Why does the value of ‘g’ vary from place to place?
Ans: We know that acceleration due to gravity is inversely proportional to the square of radius or centers and the directly proportional to the mass of the heavenly bodies. The value of radius or distance varies in different places on the same heavenly body which cause the change in value of 'g'. Similarly, if the mass of the heavenly body is large the force of attraction is also large and vice-versa that also brings in value of 'g'.
5. Where is the value of g maximum-at the equator or at poles? Why?
Ans: The value of 'g' is inversely proportional to the square of the radius of the earth's radius.  The polar radius of earth is less than the equatorial radius as the earth is not a perfect sphere. Hence, value of 'g'  is more at pole than at equator.
6. Where will the body weight be more - at a high mountain or at the sea level? Why?
Ans: Weight of a body is the product of mass of the body and acceleration due to gravity and acceleration due to gravity depends on the radius of the planet. Acceleration due to gravity increases when radius of the planet decreases and vice-versa. In case of earth radius of at a high mountain is more than at sea level, so the value of acceleration due to gravity will be more at sea level than at high mountains. Likewise, weight will be more at sea level than at mountains.
7. What will happen to the gravitational force of attraction between two bodies when the mass of  each is doubled and the distance between them is tripled? 
Ans: Let us consider the two masses m1 and m2 are place at distance d. Then the force of attraction between the two masses is given by,

$F=\frac{G{{m}_{1}}{{m}_{2}}}{{{d}^{2}}}$..........1

Again, when the two masses are doubled and the distance is tripled then the force of attraction will be, 

$F'=\frac{G2{{m}_{1}}2{{m}_{2}}}{{{(3d)}^{2}}}$

or, $F=\frac{4G{{m}_{1}}{{m}_{2}}}{9{{(d)}^{2}}}$..........2

Comparing equation we get, 

$F'=\frac{4}{9}F$.............3

Hence, equation (3) shows that force will be decreased by 4/9 times when masses doubled and distance is tripled. 

8. If an iron ball and a feather are dropped simultaneously from the same height in vacuum, which one will strike the ground first and why? 

Ans: If an iron ball and a feather are dropped simultaneously from the same height in vacuum, both will strike the ground at the same time because acceleration due to gravity is independent of the mass of the falling bodies. As, 

$g=\frac{G{{M}_{1}}}{{{d}^{2}}}$

9. What is gravity? What are the two factors that affect the gravity? 
Ans. Gravity is the gravitational force of attraction between the planet or a satellite with an object on or near to the surface of the the planet or a satellite. The two factors that affect gravity are mass of the planet and distance between the planet and the object.
10 What is gravitational field intensity? What will be the weight of a body with mass 20 kg when it is at the gravitational field intensity of 15 N/kg.

Ans: Gravitational field intensity at a point is defined as the force experienced by unit mass kept at that point from the heavenly body. It is denoted by letter ‘I’. Its SI unit is N/Kg.
We know that,
Weight of a body W= I × m
So, W= 15 ×20
Or, W = 300 N.

11. When an object falls to the ground, only the object moves down. Why is the earth’s motion not noticeable?

Ans: When an object falls to the ground only the object moves down but earth’s motion is not noticed because the mass of earth is very large in comparison to the mass of the falling object. Earth also moves towards the falling object according to Newton’s universal law of gravitation but the motion is so small that it cannot be felt or noticed, that means the motion of earth towards the object is negligible or nearly zero.
12. Can the condition of weightlessness be called masslessness? Explain. 
Ans: The condition of weightlessness be cannot be called masslessness because mass is a constant physical quantity, it remains constant everywhere but weight is a kind of force which is given by the product of mass and acceleration due to gravity. Weight of a body becomes zero when the acceleration due to gravity is zero or the acceleration of  the falling body is equal to the acceleration due to gravity i.e  g = a.
13. What is free fall? In which condition F = G? Explain. 
Ans: When an object is falling towards the surface of the planet or heavenly body under the effect of gravity without any external resistance, the fall of the body is called free fall.

When two bodies of masses 1kg each are kept a distance of 1m apart at that condition force of attraction ‘F’ is equal to the gravitational constant ‘G’. 

14. Why does tide occur in the ocean but not in Fewa Lake? 
Ans: Tides are formed by the gravitational pull of the sun and moon. These waves are very long in wavelength. Tides cannot occur in Fewa Lake because Fewa lake is very small in comparison to the ocean, so the waves cannot be formed in small lakes like Fewa lake. In other words the wave formed by gravity in lake is much longer than the lake itself.
15. How are the people living in America, just opposite to Nepal and a person in Nepal both have head faced out to the sky while standing on the surface? 
Ans: Earth is a massive object than the people living on it, so it pulls the every object towards its center on or near to its surface including human. The force exerted by earth to the object is always directed towards the center and the shape of earth is spherical due to which it pulls people just like a magnet attracts a nail, so people living in America, just opposite to Nepal and a person in Nepal both have head faced out to the sky while standing on the surface.
16.What happens to the weight of a body when it is falling freely under the action of gravity?
Ans: The weight of a body becomes zero when it falls freely under the action of gravity because the acceleration of freely falling object is equal to the acceleration due to gravity.
17. Why the mass of Jupiter about 319 times and radius is is 11 times greater than that of the Earth had radius is 11 times that of Earth. But still the gravity of Jupiter is only 2 times greater than that of the Earth. Why?
Ans: The mass of Jupiter about 319 times and radius is 11 times greater than that of the Earth had radius is 11 times that of Earth because gravitational field intensity depends not only on the mass but also the radius of the planet or heavenly body. The radius of earth is much smaller than that of Jupiter. So, the gravitational field intensity of the Jupiter is not large even though the mass of the Jupiter is 319 times more than that of earth.
18.Explain the variation of ‘g’ with height and depth.
Ans:
i. First case: At certain height: -
If we consider the radius of the earth be 'R' at the surface 'h' be the distance at certain height above the surface of the earth. Then the total distance between the center of the earth and the point at certain height 'h' be (R+h). Then,
Acceleration at surface of the earth is $g=\frac{GM}{{{R}^{2}}}$  ........................a
Acceleration at certain height 'h' is ${{g}^{'}}=\frac{GM}{{{(R+h)}^{2}}}$......................b
Putting the value of GM=gR2 from equation (a) in equation (b) we get,

$g={{g}^{'}}\frac{{{R}^{2}}}{{{(R+h)}^{2}}}$

ii. Second case: At certain depth:-
If we consider the earth to be a perfect sphere of mass M and radius R. Let 'P' be any point 'x' under the surface of the earth.Then acceleration due to gravity at point 'p' will be,
$g=\frac{GM}{{{(R-x)}^{2}}}$
Here, R-x is less than R, so the value of 'g' under the surface is less than at the surface.
19.What is the weight of a body at the center of the earth? ’Why?
Ans: The weight of a body at the center of the earth will be zero because the value of 'g' at center of the earth is zero. Weight of a body is product of mass the object and acceleration due to gravity. So, where there is acceleration due to gravity is zero there will be no weight.
20.What are the two consequences of the gravitation?
Ans: The two consequences of the gravitation are:
    i. Existence of atmosphere around a planet
    ii. Existence of solar system.
21.Why the effect of gravitation is more in liquid than in solid?
Ans: the effect of gravitation is more in liquid than in solid because the inter-molecular force of attraction is less in liquids and is weak than that of solid. So, gravitational force readily can show its effect in liquid than in solid.

3 marks questions:

1. Mention the effects of gravity.
Ans. The effects of gravity are:
    i. It produces acceleration
    ii. It holds atmosphere around the earth or a planet.
    iii. We are able to walk, jump, run and make any construction on the surface of the earth.
2. The weight of an object is more at the poles than the equator. Why?
Ans. The weight of a body is given by the product of its mass and acceleration due to gravity 'W=mg', so it is obvious that an object will have its maximum weight at the poles and least weight at the equator, as the value of 'g' depends inversely with the radius of the planet.
3. At what condition a coin and a feather fall together? What is the acceleration of the feather and the coin at that instant? Justify your answer.
Ans. Feather and coin fall together when the there is no air resistance. When two bodies falls together at the same time in the absence of any resistance the acceleration of the two bodies equal to the acceleration produced by the pull of the gravity i.e. a = g.
4. A feather and a coin when dropped from a height on the surface of the moon, fall simultaneously, why?
Ans. There is absence of atmosphere in the surface of moon because the value of acceleration due to gravity in case of moon is small in comparison the earth. So, moon can not hold atmosphere around it. When feather and coin is dropped simultaneously from a certain height, they fall together and hit the ground at the same time due to the absence of the air resistance.
5. The fall of parachute towards of earth’s surface is not free fall. Justify this statement.
Ans. When a a parachute jumper dives from a height, the parachute jumper will fall under the action of gravity, however, after the parachute is open, the jumper will stat to fall with uniform velocity because of air resistance. Under such condition the acceleration produced by the falling jumper becomes zero. This helps the parachute jumper to land safely on the ground.
6. It is difficult to lift a large stone on the surface of the earth but easy to lift a smaller one, why?
Ans: The large stone has greater mass then small stone. The weight of large stone is more than that of small one because weight is the product of mass of an object and the acceleration due to gravity. Therefore,it is difficult to lift a large stone on the surface of the earth but easy to lift small one.
7. How much mass can a person lift on the surface of moon if he can lift 100 Kg on the surface of the earth?
Ans: Solution,
   In case of earth,
   Mass of an object (Me) = 100kg
   Acceleration due to gravity (g) = 9.8 m/s2
   Weight of an object (W) = ?
We have,
   W = m×g
   W = 100 × 9.8
   W= 980 N
Again,
   In case of the moon,
   Weight of an object (W) = 980N
   Acceleration due to gravity (g) = 1.67 m/s2
   Mass of an object (Mm) = ?
We have,
   W = m × g
or, 980 = Mm ×1.67
or, Mm = 980/1.67
or, Mm = 586.8 kg
Therefore, the person can lift 586.8 kg mass on the surface of the moon. 

8. Study the given diagram and calculate the gravitational force between these physical masses.

Ans: 

9. Describe in brief about the feather and coin experiment and write its conclusion.
Ans: When Galileo performed the experiment with feather and coin, he found that feather fell more slowly than the coin. It was found that feather fell slowly due to the air resistance when Newton performed the experiment in both in vacuum and air, he noticed that both the coin and feather fell simultaneously inside the vacuum due to the absence of air resistance. 
Hence, the final conclusion of the experiment was acceleration due to gravity is independent of the mass of the falling body in vacuum. 
10. Prove that acceleration due to gravity and weight of a body are inversely proportional.
Ans: Consider 'R' be the radius and 'M' be the mass of the earth. An object with the mass 'm' is on the surface of the earth, so the distance between the centere of the earth and the object on the surface will be 'R'. According to Newton'w law of gravitation,
$F=\frac{GMm}{{{R}^{2}}}$................a
Again, 

If 'g' is acceleration produced on an object when it falls down, then 

From Newton's second law of motion, 

F = ma ......................b

From equation a and b, we get,

or, $mg=\frac{GMm}{{{R}^{2}}}$

or, $g=\frac{GM}{{{R}^{2}}}$

or, $g\alpha \frac{1}{{{R}^{2}}}$ ..............c   [Being, G and M are constants]

Equation 'c' shows that acceleration due to gravity is inversely proportional to the square of the radius of the earth.
11. Prove that:$F=\frac{G{{m}_{1}}{{m}_{2}}}{{{d}^{2}}}$
Ans:Newton’s law of gravitation states that “The force of gravitation between two masses or bodies anywhere in the universe is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers”.

It is called universal law because this law holds true for all the bodies, whether it is massive or microscopic placed anywhere in the universe. The effect of gravitation is more in liquid than in solid because inter-molecular force of attraction is less in liquid and it is weaker than in solid.

Consider, two bodes with mass m₁ and m₂ which are 'd' distance apart from their centers.

According to Newton’s law of gravitation,

$F\alpha {{m}_{1}}{{m}_{2}}$..............................1

$F\alpha \frac{1}{{{d}^{2}}}$...............................2

Combining equation 1 and 2 we get,

Or, $F\alpha \frac{{{m}_{1}}{{m}_{2}}}{{{d}^{2}}}$.....................3

Therefore, $F= \frac{G{{m}_{1}}{{m}_{2}}}{{{d}^{2}}}$......................................4

Where, G is a proportionality constant which is commonly known as universal gravitational constant and its value is 6.67×10 -11 Nm²kg ^{– 2} .

12. Prove that acceleration due to gravity is independent of mass of an object.

Or,

13. Prove that:$g=\frac{Gm}{{{R}^{2}}}$ or, $g\alpha \frac{1}{{{R}^{2}}}$

Ans: Let us consider the mass of earth be 'M' and an object is place on the surface of  the earth. The distance between their centers be 'R' which is nearly equal to the radius of the earth.

According to Newton's law of gravitation;

 $F=\ \frac{G{{m}_{1}}{{m}_{2}}}{{{R}^{2}}}$  .........i

or, $mg=\frac{GMm}{{{R}^{2}}}$                      [$\because $F=W=mg]

Where, 
            M=mass of earth
            R=Radius of earth
            W=Weight of the object
            G=Gravitational constant= 6.67×10 -11 Nm²kg ^{– 2}

or, $g=\frac{GM}{{{R}^{2}}}$

or, $g\alpha \frac{GM}{{{R}^{2}}}$...................ii

Here, equation (ii) shows that gravity of a planet is directly proportional to the Mass of the planet or satellite (M) that means if the radius of the planet is increased keeping mass M constant, the gravity will be less and if the radius is decreased, the gravity will increase. 
Equation (ii) also shows that acceleration due to gravity is independent of mass of and object.

4 marks questions:
1.What is the change in the gravitational force between two bodies if the distance between them is halved, keeping their masses constant?

Ans:Let us consider two masses m1 and m2 are kept at a distance d from their centers. According to Newton's universal gravitational law, the force between two masses is:

$F=\frac{G{{m}_{1}}{{m}_{2}}}{{{(d)}^{2}}}$ .............a

Again,
If the distance between two masses is halved, the force of between the bodies will be,

\[F'=\frac{G{{m}_{1}}{{m}_{2}}}{{{\left( \frac{1}{2}d \right)}^{2}}}\]

\[F'=\frac{G{{m}_{1}}{{m}_{2}}}{\frac{{{d}^{2}}}{4}}\]

${F}'=4\frac{G{{m}_{1}}{{m}_{2}}}{{{d}^{2}}}$............b

Comparing equation (a) and (b),we get,

${F}'=4F$................c          [ from equation (a)]

Equation (c) shows that the force will increase four time when distance between the two masses is halved keeping their masses constant.
2. Tides rise on the sea, why? What is weightlessness? Prove that acceleration due to gravity is independent to the mass of the falling object.

Ans: Tides are formed by the gravitational pull of the sun and moon. These waves are very long in wavelength. Tides cannot occur in lake or pond because lake or ponds are very small in comparison to the ocean, so the waves cannot be formed in lakes or pond. In other words the wave formed by gravity in lake is much longer than the lake itself.
Weightlessness is the condition in which the weight of an object seems to be zero.

Let us consider the mass of earth be 'M' and an object is place on the surface of  the earth. The distance between their centers be 'R' which is nearly equal to the radius of the earth.

According to Newton's law of gravitation;

 $F=\ \frac{G{{m}_{1}}{{m}_{2}}}{{{R}^{2}}}$  .........i

or, $mg=\frac{GMm}{{{R}^{2}}}$                      [$\because $F=W=mg]

Where, 
            M=mass of earth
            R=Radius of earth
            W=Weight of the object
            G=Gravitational constant= 6.67×10 -11 Nm²kg ^{– 2}

or, $g=\frac{GM}{{{R}^{2}}}$

or, $g\alpha \frac{GM}{{{R}^{2}}}$...................ii

Here, equation (ii) shows that gravity of a planet is directly proportional to the Mass of the planet or satellite (M) that means if the radius of the planet is increased keeping mass M constant, the gravity will be less and if the radius is decreased, the gravity will increase.
Equation (ii) also shows that acceleration due to gravity is independent of mass of and object.

3. The earth revolves around the sun in the elliptical orbit as shown in the given figure. What happens in the gravitational force of the sun when the earth moves from point A to point B? Explain why the earth revolve around the sun?
Ans: 

4. Study the given figure and answer the following:

            i. Calculate the force of attraction between A and B.

            ii.If mass of A is doubled keeping the distance constant, what effect will be
               seen on the force of attraction?

            iii. If the distance between them is doubled keeping the masses constant, what effect
                 will be seen on force of attraction?

Numerical