2 Marks Question
 Kathmandu lies at high altitude than Biratnagar from sea level. Where does an object have more weight between two places? Give reason.
 The weight of an object is more in Biratnagar than in Kathmandu because the weight of the object depends on the acceleration due to gravity. As Biratnagar is in a low place its value of acceleration due to gravity is high and the higher the value of acceleration due to gravity, the heavier will be the object.
 When a man travels from the Hilly region to the Terai region, what will happen to his weight? Explain with reasons.
 The radius of the earth is less in the terai than in the hills. So, the value of acceleration due to gravity is higher in the Terai than in the hills. (g ∝ $\frac{1}{R^2}$) And, acceleration due to gravity is directly proportional to the weight. Hence, when a man travels from the Hilly region to the Terai region his weight increases.
 Illustrate the relation g ∝ $\frac{1}{R^2}$ with an example.
 Value of 'g' decrease with an increase in the radius of the planet and viceversa. The value of 'g' becomes more at the poles (Shorter radius) of the earth and its value is less at the equator (longer radius) of the earth.
 Clarify the statement, "acceleration due to gravity of the earth is 9.8 m/s^{2}"
 The velocity of a freefalling body forwards the earth's surface increases by 9.8 m/s in each second.
 How much is the weight of a body less on the moon surface than on the earth surface? Why?
 Moon is smaller than the earth so its gravity is 1/6 times less than earth. Thus, the weight of anybody on the moon is 1/6 times less than on the earth.
 Why is the value of 'g' more in Terai than in the mountain?
 The radius of the earth is less in the Terai than in the hills. The lower the radius of the earth, the higher the value of gravity. (g ∝ $\frac{1}{R^2}$) Therefore, the value of acceleration due to gravity is higher in the Terai than in the hills.
 A large stone of 20 kg and small stone of 5 kg are dropped simultaneously from certain height. Which one reaches on the ground first?
 The stone with both small and large masses hit the ground at the same time. It is because the magnitude of the acceleration due to gravity is equal to all the freely falling bodies. g does not depend upon the masses.
 What happens to the weight of an object when it is carried from the earth to moon, why?

We know,
weight = mass × acceleration due to gravity
w ∝ g (m is constant)
When an object is carried from the earth to moon the weight of the body decreases because the value of acceleration due to gravity of moon is 1/6 times less than that of earth. i.e. if the weight of an object in earth is 6 N then the weight of the object in moon is only 1 N.  The acceleration due to gravity on the surface of the Jupiter is 25 m/s^{2}. What does it mean?
 The acceleration due to gravity on the surface of the Jupiter is 25 m/s^{2}. The statements mean that when the body falls in the surface of Jupiter its velocity increase by 25 m/s in every second.
 Write any two difference between gravity and acceleration due to gravity (g).

Difference between gravity and acceleration due to gravity are shown below
in table:
Gravity Acceleration due to gravity The force of an object attracting another object to its center is called gravitational force. Acceleration produced in a freely falling object due to the presence of gravity is called acceleration due to gravity. It depends upon the masses of two objects and distance between their centers. It depends upon the masses and radius of the planet or satellite. It is measured in Newton. It is measured in m/s^{2}.  Why iron ball and a feather fall together in a vacuum ?
 Iron ball and a feather fall together in a vacuum because in vacuum there is no up thrust and we know acceleration produced in the freely falling bodies is same for all. It does not depend upon the masses. Hence, they fall together in vacuum.
 Why does the value of g is more in polar region than in equator?

The Earth is not a perfect sphere. It flattens at the poles and bulges out
at the equator, So, the radius of the earth is not same at all place.
We know, acceleration due to gravity is inversely proportional to the square of the radius i.e.
g ∝ 1/R^{2}
Hence, the value of g is more in polar region than in equator.  Why does the weight of body is more at polar region than at the equator?
 The Earth is not a perfect sphere. It flattens at the poles and bulges out at the equator. The radius of the earth is more at the equator and less at the poles of the Earth. So, g is more at the pole and less at the equator (g ∝ $\frac{1}{R^2}$). And we know, w ∝ g Hence, the weight of body is more at polar region than at the equator.
 Why can't we fall safely with the help of parachute towards the moon?
 There is no atmosphere in the moon. So, the falling parachute does not experience any air resistance on the moon and it falls with greater velocity. Hence, we can't fall safely with the help of parachute towards the moon.
 What changes occurs in the gravitational force between two bodies when mass of each body is made doubled and distance between their center is halved?

The force of gravitation between two bodies is given by,
F = $\frac{Gm_{1}m_{2}}{d^2}$  (i)
When the masses of both bodies are doubled and the distance between their center is halved, their masses become 2m_{1} and 2_{2} and the distance become d/2.
Now, F_{1} = $\frac{G(2m_{1})(2m_{2})}{(d/2)^2}$
or, F_{1} = $\frac{4Gm_{1}m_{2}}{(d/2)^2}$
or, F_{1} = $\frac{4Gm_{1}m_{2}}{d^2/4}$
or, F_{1} = $\frac{16Gm_{1}m_{2}}{d^2}$or, F_{1} = 16F (from i)
Hence, if the masses of both bodies are doubled and the distance between their center is halved, the force of gravitation increases by 16 times the original force of gravitation.
 Under which condition the value of gravitational force and gravitational constant becomes equal?

When two objects of unit masses are separated by a unit distance, the force
of gravitation is equal to gravitational constant. i.e. at m_{1} =
m_{2} = 1 kg and d = 1 m.
Then, F = $\frac{Gm_{1}m_{2}}{d^2}$
So, F = G.  Write the difference between freefall and weightlessness.

The difference between freefall and weightlessness is shown below in table:
Freefall Weightlessness The fall of a body under the effect of gravity in the absence of external resistance is called freefall. When a body falls freely under the effect of gravity, the weight of the body appears to be zero. This state of the body is weightlessness. In every free fall there is weightlessness. For every weightlessness there may not be freefall.  The weight of a body is less on the moon surface than on the earth surface, why?

We know,
w = mg
w ∝ g (m is constant)
From above we can see that acceleration due to gravity is directly proportional to the weight. Value of g of earth (9.8 m/s^{2}) is greater than the value of g of moon (1.6m/s^{2}). So, the weight of a body is less on the moon's surface than on the earth's surface.  A stone and piece of paper are dropped simultaneously from the same height on the lunar surface, which one will fall faster, why?
 If a stone and piece of paper are dropped simultaneously from the same height on the lunar surface they will fall simultaneously because there is an absence of external resistance in lunar surface. And, we know g is same for all, it is independent of masses of any bodies.
 Write the differences between acceleration due to gravity and gravitational constant.

The differences between acceleration due to gravity and gravitational
constant are shown below in table:
Acceleration due to gravity Gravitational Constant It is an acceleration produced on a freely falling body due to influence of gravity. The force of attraction existing between twounit masses separated by a unit distance is called gravitational constant. The value of 'g' varies from place to place. Its value remains constant everywhere. It is a vector quantity. It is a scalar quantity. Its SI unit is m/s^{2}. Its SI unit is Nm^{2}/kg^{2}.  The value of acceleration due to gravity varies according to place of the earth, why?

The Earth is not a perfect sphere. It flattens at the poles and bulges out
at the equator, So, the radius of the earth is not the same at all place.
We know, that acceleration due to gravity is inversely proportional to the square of the radius i.e.
g ∝ $\frac{1}{R^2}$
Hence, the value of g varies according to place of the earth.  When a feather and a coin are dropped towards the surface of earth, do they reach ground together? If this experiment is done in moon, what differences occurs? Write with reasons.

When a feather and a coin are dropped towards the surface of earth, the coin
falls faster than the feature because due to the presence of air resistance
on the earth it retards the velocity of a lighter body with more surface area.
Similarly, if the same experiment is done in moon they will fall simultaneously because there is no air resistance due to the absence of atmosphere. And we know, acceleration due to gravity is the same for all bodies.  The acceleration due to gravity on the surface of the earth is 9.8 m/s^{2}. What is its meaning? What is the main conclusion of the Galileo's "feather and coin experiment"?

The acceleration due to gravity on the surface of the earth is 9.8
m/s^{2}. The statements mean that when the body falls on the surface
of earth, its velocity increases by 9.8 m/s every second.
The main conclusion of the Galileo's "feather and coin experiment" is that, If there is no external resistance, different bodies dropped from the same height fall at the same speed.  In which condition do a feather and a coin dropped from the same height fall at the same speed, why?
 If there is no external resistance then a feather and a coin dropped from the same height falls at the same speed because the acceleration produced in the freely falling bodies is same for all bodies and it does not depend on the mass of the falling bodies.
 Where does the weight of a body become maximum in Nepal? Why?

We know, w = mg
w ∝ g (m is constant)
And, we know g is inversely proportional to the height. So, the weight of the body is maximum in Nepal where there is the low height (that is, in terai region).  Why does the sheet of paper fall later on the earth's surface than the paper ball of equal weight if thrown from a certain height?
 Due to the presence of air resistance on earth, it retards the velocity of the body with more surface area. The surface area of the sheet of paper is larger than the paper ball. Hence, the sheet of paper fall later on the earth surface than the paper ball of equal weight if thrown from a certain height.
 A satellite does not need any energy to revolve around the earth, why?
 A satellite does not need any energy to revolve around the earth because of the balanced centripetal and centrifugal forces provided by the gravitational force.
 The weight of the object is more at polar region than equatorial region, why?

We know,
weight = mass × acceleration due to gravity
w ∝ g (m is constant)
The value of g is maximum at pole (9.83 m/s^{2}) than at equator (9.78 m/s^{2}). So, the weight of a body is maximum in the polar region of the earth because from the above relation we can see, that g is directly proportional to weight.  Write the difference between gravity and gravitation.

The difference between gravity and gravitation is shown below in table:
Gravity Gravitation The force of an object attracting another object to its center is called gravity. The mutual force of attraction between two bodies is called gravitation. It requires only one mass. It requires two masses. It is a strong force. It is a weak force. For example: When we jump, we land on the ground. For example: the force we are applying on every other object on Earth right now.  What effect will be on acceleration due to gravity if radius of the earth is decreased?

We know,
g = $\frac{G.m}{R^2}$
g ∝ $\frac{1}{R^2}$
Here, we can see that, acceleration due to gravity is inversely proportional to square of radius. Hence, if radius decreases then acceleration due to gravity increases.  We do not get hurt, when we jump with parachute, why?
 Due to the presence of air resistance in earth it retards the velocity of body with more surface area. The body falling with parachute has large surface area so it experiences larger air resistance. So, body falls slowly with uniform velocity and hence land safely.
 The probability of getting hurt when a man jumps from a greater height, why?
 Acceleration due to gravity is produced on a freely falling body. Due to this, when a man jumps from a significant height, he will have enough time to attain maximum velocity before he reaches the ground. Due to this, the man will have high kinetic energy and strikes the ground with great force. Therefore, there is more probability of getting hurt when a man jumps from a greater height.
 Write difference between mass and weight.

The difference between mass and weight is shown below in table:
Mass Weight The quantity of matter contained in a body is mass. The total force of gravity acting on a body is weight. It does not change from place to place. It is variable quantity. t is measured in kg. It is measured in Newton. It is scalar quantity. It is measured by using beam balance. It is vector quantity. It is measured by using spring balance.  If a stone of 1 kg and 5 kg masses are dropped in the lunar surface from the same height, which one will reach on the surface faster and why?
 If a stone of 1 kg and 5 kg masses are dropped on the lunar surface from the same height both will reach the surface at the same time because there is no air resistance due to the absence of an atmosphere. And we know, that acceleration due to gravity is the same for all bodies.
 What is the difference between fall of parachute on the earth and that on the moon? What is the effect of gravity on falling objects?

The difference between fall of parachute on the earth and that on the moon
is shown below in table:
Parachute fall on earth Parachute fall on moon Up thrust of air acts on the parachute. Up thrust of air does not act on the parachute. Free fall is not experienced. Free fall and weightlessness is experienced.  Write two factors that affect the gravitational force.

The two factors that affect the gravitational force are:
 Product of the masses of bodies.
 Distance between bodies from their center.
 When a person jumps from the airplane with parachute can land safely on the earth surface but it is not possible on the moon, why?

When one jumps with a parachute on the earth, due to the air resistance it
retards the motion of the parachute and it falls with slow and uniform velocity.
So, person land safely.
Similarly, there is no atmosphere on the moon. So, the falling parachute does not experience any air resistance and it falls freely.  At what condition does a coin and a feather fall together? What is the acceleration of the feather at the coin at that instant?
 If there is no air resistance, a coin and a feather fall together. At that instant, both have the same acceleration.
 It is difficult to lift a large stone on the surface of the earth but easy to lift small one, why?
 It is so because large stone has more force of attraction of the earth as it has more mass (i.e. F = mg) But, the smaller one has less force of attraction as it has less mass. So, it is easier to lift a small stone than a large stone.
 What is centripetal and centrifugal fore?

Centripetal force is the force acting towards the centre of the circular
path. It is the net force towards centre.
F_{c} = $\frac{mv^2}{r}$
And, Centrifugal force is the force acting in a direction away from the centre of the circle.
F_{cf} =  $\frac{mv^2}{r}$Where, F_{c} = centripetal force
F_{cf} = centrifugal force
m = mass
v = velocity
r = radius