NCERT Solutions for Class 9th Science
Chapter 10 – GRAVITATION
(Complete Downloadable Chapter Solution PDF file is at the bottom of the page)
Q.1 State the universal law of gravitation.
Q.2 Write the formula to find the magnitude of the gravitational force between the earth and an object on the surface of the earth.
Ans Let mass of earth = M kg
Let mass of the object on the surface of earth = m kg
Let the radius of earth = R m
From Universal law of gravitaion,
Gravitational force between them, F = GMm/R2 (where ‘G’ is the universal gravitational constant with value 6.67 X 10-11 N m2 kg-2).
Q.3 What do you mean by free fall?
Ans Free fall may be defined as the fall under gravity alone i.e. an object falling towards the earth under gravitational force alone, is said to be in free fall.
Q.4 What do you mean by acceleration due to gravity?
Q.5 What are the differences between the mass of an object and its weight?
Q.6 Why is the weight of an object on the moon 1/6th its weight on the earth?
Q.7 Why is it difficult to hold a school bag having a strap made of a thin and strong string?
Q.8 What do you mean by buoyancy?
Ans Buoyancy: It may be defined as the upward force exerted by the fluid on an object immersed in it. The magnitude of this buoyant force depends on the density of the fluid.
Q.9 Why does an object float or sink when placed on the surface of water?
Ans Objects will float or sink in water depending on their density. Objects of density less than that of water float on it whereas objects of density greater than that of water sink in it.
Q.10 You find your mass to be 42 kg on a weighing machine. Is your mass more or less than 42 kg?
Q.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?
Ans The bag of cotton will be heavier. This is due to more upthrust of air acting on bag of cotton as its volume is more than the iron bar of 100kg. The upthrust on cotton bag reduces the reading on a weighing machine which is actually heavier.
EXERCISES
Q.1 How does the force of gravitation between two objects change when the distance between them is reduced to half ?
Ans Force of gravitation, F = Gm1m2/d2 (where m1,m2 are the masses of objects and d is the
distance between them)
Now if the distance is reduced to half,
New force of gravitation, F’ = Gm1m2/(d/2)2 = 4 Gm1m2/d2 = 4F
Hence the force of gravitation between two objects will become 4 times.
Q.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?
Ans Objects fall under acceleration due to gravity ‘g’ which does not depend on the mass. Hence both heavy and light objects fall at the same rate.
Q.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 × 106 m.)
Q.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?
Q.5 If the moon attracts the earth, why does the earth not move towards the moon?
Ans Earth and moon attract each other with the same force i.e. force of gravitation. But according to the second law of motion, for a given force, acceleration is inversely proportional to the mass of an object and the mass of moon is very small compared to that of the earth. Hence we do not see the earth moving towards the moon.
Q.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?
Ans Force between two objects with masses m1 and m2 and having distance ‘d’ between them is given by, F = Gm1m2/d2(where G = 6.67 X 10-11 N m2 kg-2 is the gravitational constant)
(i) If the mass of one object is doubled,
New mass m1’ = m1, m2’ = 2m2, d’ = d
Therefore new force, F’ = Gm1’m2’/d’2 = Gm1(2m2)/ d2 = 2 (Gm1m2/d2) = 2F
Hence the force will become twice.
(ii) If the distance between the objects is doubled
F’ = Gm1m2/(2d)2 = (Gm1m2/d2) = F/4
Hence the force will become 1/4 times.
If the distance between the objects is trippled
F’ = Gm1m2/(3d)2 = (Gm1m2/d2) = F/9
Hence the force will become 1/9 times.
(iii) If the masses of both objects are doubled
F’ = G(2m1)(2m2)/d2 = 4 (Gm1m2/d2) = 4F
Hence the force will become 4 times.
Q.7 What is the importance of universal law of gravitation?
Q.8 What is the acceleration of free fall?
Ans It will be acceleration due to gravity i.e g = 9.8 m/s.
Q.9 What do we call the gravitational force between the earth and an object?
Ans Weight of the body.
Q.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.]
Q.11 Why will a sheet of paper fall slower than one that is crumpled into a ball?
Q.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 newtons of a 10 kg object on the moon and on the earth?
Q.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.
Q.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.
Q.15 A stone is thrown vertically upward with an initial velocity of 40 m/s. Taking g = 10 m/s2, find the maximum height reached by the stone. What is the net displacement and the total distance covered by the stone?
Q.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.
Q.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.
Q.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.
Q.19 In what direction does the buoyant force on an object immersed in a liquid act?
Q.20 Why does a block of plastic released under water come up to the surface of water?
Q.21 The volume of 50 g of a substance is 20 cm3. If the density of water is 1 g/cm3, will the substance float or sink?
Q.22 The volume of a 500 g sealed packet is 350 cm3. Will the packet float or sink in water if the density of water is 1 g/cm3? What will be the mass of the water displaced by this packet?