Question 1.
State the universal law of gravitation.
Solution:
According to universal law of gravitation, every particle in the universe attracts every other particle with a force which is directly proportional to the product of their masses and inversely proportional to the square of distance between them. The direction of force is along the line joining the two particles.

Question 2.
Write the formula to find the magnitude of the gravitational force between the earth and an object on the surface of the earth.
Solution:
The formula for the magnitude of gravitational force between the earth and an object on its surface is,  where F is the gravitational force. G is the gravitational constant. M_e is the mass of the earth. m is the mass of the object on the surface of the earth. R_e is the radius of the earth.

Question 3.
What do you mean by free fall?
Solution:
All objects falling towards earth under the action of gravitational force of earth alone are said to be in free fall.

Question 4.
What do you mean by acceleration due to gravity?
Solution:
The acceleration with which an object fall freely towards the earth is known as acceleration due to gravity. It is denoted by g and its value is 9.8 m s^-2.

Question 5.
What are the differences between the mass of an object and its weight?
Solution:

Mass	Weight
1.	Mass of a body is the measure of its inertia.	Weight of the body is the force with which it is attracted towards the earth (W = m x g).
2.	Its S.I. unit is kg.	Its S.I. unit is Newton.
3.	It remains constant everywhere.	Its value changes from place to place.
4.	It is measured by common balance.	It is measured by spring balance.

Question 6.
Why is the weight of an object on the moon  its weight on the earth?
Solution:
The weight of an object depends on the value of acceleration due to’gravity g. The value of g on earth is 6 times more than that of moon because, the mass and radius of the earth is more than the mass and radius of the moon.

Weight of a body of mass m on moon is

Question 7.
Why is it difficult to hold a school bag having a strap made of a thin and strong string?
Solution:
We know that pressure = force/area. When the string of the school bag is thin, its area is small and as such the pressure exerted on the shoulders or the hands supporting the bag is large. lip this case, the force acting on the shoulders or the hand which support the bag is equal to the weight of the bag. In case, the strap is broad as is usually the case, the area on which the force (weight of the bag) acts is large and the pressure is reduced as the weight of the bag is now distributed over a larger area.

Question 8.
What do you mean by buoyancy?
Solution:
Whenever an object is immersed in a liquid, either partially or fully, an upward force is exerted on the object by the liquid. This upward force is called upthrust or buoyant force or force of buoyancy and the property of the fluid due to which this upthrust is exerted on the object is called buoyancy.

Question 9.
Why does an object float or sink when placed on the surface of water?
Solution:
When the object has density less than 1 g cm^-3 (density of water), then it floats on the surface of water, because, it always displaces more weight of water than its own weight. As buoyant force is more than its own weight, therefore, it floats. When the object has density more than 1 g cm-3, then it sinks in water, because it always displaces less weight of water than its own weight. As buoyant force is less than its own weight, therefore, it sinks.

Question 10.
You find your mass to be 42 kg on a weighing machine. Is your mass more or less than 42 kg?
Solution:
A weighing machine is a sort of spring balance which measure the weight and not the mass of a body. When we stand on the weighing machine, our weight which is due to gravitational attraction of the earth acts vertically downwards. But the buoyancy due to air on our body acts vertically upwards. As a result of this, our apparent weight true weight – buoyant force is less than the true weight. Since the weighing machine measures the apparent weight, our true weight is more, i.e., more than 42 kg.

Question 11.
You have a bag of cotton and an iron bar, each indicating a mass of 100 kg when measured on a weighing machine. In reality, one is heavier than other. Can you say which one is heavier and why?
Solution:
We know that true weight = apparent weight + upthrust. The cotton bag is heavier than the iron bar. This is due to the reason, that the bag of cotton which has more volume (as it has less density) than the iron bar (which has more density), experiences more upthrust due to air.

NCERT Exercises

Question 1.
How does the force of gravitation between two objects change when the distance between them is reduced to half?
Solution:
Force of gravitation,


The force of gravitation becomes 4 times more.

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?
Solution:
Gravitational force acts on all objects in proportion to their masses. But a heavy object does not fall faster than a light object. This is because of the reason that

or Force = Acceleration × Mass As force is directly proportional to mass, acceleration is constant for a body of any mass.

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 × 1024 kg and radius of the earth is 6.4 × 10m)
Solution:
The ‘gravitational force between the earth and 1 kg object on us surface is given by

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?
Solution:
The earth attracts the moon with a force equal to the force with which the moon attracts the earth. This is because as per Newton’s third law of motion, forces of action and reaction are always equal and opposite.

Question 5.
If the moon attracts the earth, why does the earth not move towards the, moon?
Solution:
Both the earth and the moon attract each other with the same force. But according to Newton’s second law of motion, acceleration produced in a body by any force is inversely proportional to the mass of the body. Since, mass of the earth is much more than that of the moon, the acceleration produced in the earth is negligible. As a result, it appears as if the earth does not move towards the 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?
Solution:
From the relationship,

(i) If the mass of one object (say body 1) is doubled, then

Thus, the gravitational force between the two objects gets doubled.
(ii) If the distance between the two objects is doubled, then

Thus, the gravitational force between the two objects becomes one-fourth.
If the distance between the two objects is tripled, then

Thus, the gravitational force between the two objects becomes one-ninth.
(iii) If the masses of both the objects are doubled, then

Thus, the gravitational force between the two objects becomes 4 times.

Question 7.
What is the importance of universal law of gravitation?
Solution:
Universal law of gravitation is important as it accounts,
(a) for the existence of the solar system, i.e., motion of planets around the sun.
(b) for holding the atmosphere near the surface of the earth.
(c) for the flow of water in rivers.
(d) for rainfall and snowfall.
(e) for occurrence of tides.

Question 8.
What is the acceleration of free fall?
Solution:
All objects moving towards earth on account of gravitational force of earth on them are said to be in free fall. This force produces a uniform acceleration in the object. This is acceleration of free fall and its value is 9.8 m s^-2.

Question 9.
What do we call the gravitational force between the earth and an object?
Solution:
The gravitational force between the earth and an object is called the force of gravity or simply earth’s gravity.

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?
Solution:
We know that the value of g is greater at the poles than at the equator. So the weight of gold at the equator will be less than the weight of gold at the poles. So it is obvious that the friend at equator will not agree with the weight of gold bought at poles.

Question 11.
Why will a sheet of paper fall slower than one that is crumpled into a ball?
Solution:
A sheet of paper will fall slower than the one that is crumpled into a ball. This is because the air offers resistance due to friction to the motion of the falling objects. The resistance offered by air to the sheet of paper is more than the resistance offered by air to the paper ball because the sheet has larger area.

Question 12.
Gravitational force on the surface of the moon is only 1 as strong as gravitational force on 6 the earth. What is the weight in newtons of a 10 kg object on the moon and on the earth?
Solution:
Here, m = 10 kg
Mass is the same on earth and moon.
Now, weight of the object on earth,
W_e, = mg_e = 10 × 9.8 = 98 N
Weight of the object on moon, = 

Question 13.
A ball is thrown vertically upwards with a velocity of 49 m/s. Calculate
(i) the maximum height to which it rises,
(ii) the total time it takes to return to the surface of the earth.
Solution:

Question 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.
Solution:

Question 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?
Solution:

As final position of the stone coincides with its initial position, net displacement = 0 Total distance covered by the stone = h + h = 80m + 80m = 160 m

Question 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.
Solution:

Thus, the earth and the sun attract each other by a gravitational force of 3.56 × 10²² N.

Question 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.
Solution:
Here, h = 100 m.
Let the two stones meet after t seconds at a point P which is at a height x above the ground as shown in figure.


Question 18.
A ball thrown up vertically returns to the thrower after 6 s. Find
(a) the velocity with which it was thrown up,
(b) the maximum height it reaches, and
(c) its position after 4 s.
Solution:
Here, time of ascent = time of descent,

Question 19.
In what direction does the buoyant force on an object immersed in a liquid act?
Solution:
If an object is immersed in a liquid then the buoyant force due to liquid acts on the object in vertically upward direction.

Question 20.
Why does a block of plastic released under water come up to the surface of water?
Solution:
The buoyant force acting on the block of plastic is more than its weight. As a result of this, it comes up when released under water.

The cause of this larger buoyant force on the block of plastic is due to its density being lesser than that of water.

Question 21.
The volume of 50 g of a substance is 20 cm³. If the density of water is 1 g cm^-3, will the substance float or sink?
Solution:

As the density of the substance is greater than that of water, the given substance will sink in water.,

Question 22.
The volume of 500 g sealed packet is 350 cm³. 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?
Solution:
Here, mass of packet, M – 500 g volume of the packet, V = 350 cm³ Clearly, density of packet,  Since the density of packet is more than density of water, the packet will sink. As the packet is fully submerged in water, mass of water displaced by the packet = volume of the packet x density of water = 350 cm³ × l g cm^-3 = 350 g