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# Chapter 10 Gravitation

We all know the earth revolve around sun and it rotate on its own axis yet we don't feel the rotation and very surprising that we are on the crust yet we don't fall on space. This is all due to gravitation force, which holds every object on earth. Newton once saw apple falling down the tree, Question arises why this apple falls down not raised up word and small curiosity gives the concept of gravity.

Download pdf of NCERT Examplar with Solutions for Class Science Chapter 10 Gravitation

### Exercise 1

•  Q1 State the universal law of gravitation. Ans: Every object in the universe attracts every other object with a force which is proportional to the product of their masses and inversely proportional to the distance between them . For two objects of masses m1 and m2 and the distance between them r, the force (F) of attraction acting between them is given by the universal law of gravitation as: Where, G is the universal gravitation constant given by: G = 6.67 x 10-11 Nm2 kg-2 Q2 Write the formula to find the magnitude of the gravitational force between the earth and an object on the surface of the earth. Ans: The mass of the earth = m1 The mass of the object = m2 Distance between the Earth’s centre and object ( radius of Earth ) = r Therefore, Gravitational force is ### Exercise 2

•  Q1 What do you mean by free fall? Ans: A free fall motion means that the object is falling from a height under the influence of gravity only. It falls only due to its weight and not any other force. Provided these conditions the object experiences a free fall. It is observed that in a free fall; free - falling objects do not encounter air resistance. Q2 What do you mean by acceleration due to gravity? Ans: When a body falls towards the earth from a height, then its velocity changes during the fall. This changing velocity produces acceleration in the body. This is called acceleration due to gravity. Its value is given by 9.8 m/s2.

### Exercise 3

• Q1

What are the differences between the mass of an object and its weight?

Ans:
S. No. Mass Weight
1 Mass is the property of matter. The mass of an object is the same everywhere. Weight depends on the effect of gravity. Weight increases or decreases with higher or lower gravity.
2 Mass can never be zero. Weight can be zero if no gravity acts upon an object, as in space.
3 Mass can never be zero. Weight is vector quantity. It is different at different places.
4 It only has magnitude. It has magnitutde as well as direction.
5 Its SI unit is kilogram (kg). Its SI unit is the same as the SI unit of force, i.e., Newton (N).

Q2

Why is the weight of an object on the moon 1/6th its weight on the earth?

Ans:

#### RE = the radius of the Earth

WE = the object on the surface of the Earth Let, MM = mass of the moon

RM = radius of the moon

WM = the object on the surface of the moon  Where, ME = 5.98 x 1024 kg, MM = 7.36 x 1022 kg
RE = 6.4 x 106 m, RM = 1.74 x 106 m Therefore, weight of an object on the moon is 1/6 of its weight on the Earth.

### Exercise 4

•  Q1 Why is it difficult to hold a school bag having a strap made of a thin and strong string? Ans: It is difficult to hold a school bag having a strap made of thin and strong string, because the thin string has very less contact area in case of a school bag having a strap made of thin and strong string which increases pressure which is uncomfortable to carry the school bag. Q2 What do you mean by buoyancy? Ans: The upward force exerted by a liquid on an object that is partly or wholly immersed in it is known as buoyancy. Buoyancy is caused by the differences in pressure acting on opposite sides of an object immersed in a static fluid. It is also known as the buoyant force. Q3 Why does an object float or sink when placed on the surface of water? Ans: An object sinks in water if its density is greater than that of water. This is because the buoyant force acting on the object is less than the force of gravity. On the other hand, an object floats in water if its density is less than that of water. This is because the buoyant force acting on the object is greater than the force of gravity.

### Exercise 5

•  Q1 You find your mass to be 42 kg on a weighing machine. Is your mass more or less than 42 kg? Ans: The weighing machine reads slightly less than the actual value. This is because of the upthrust of air acting on our body. Hence, the body gets pushed slightly upwards, causing the weighing machine to show a reading less than the actual value. Q2 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 is heavier than the iron bar. This is because the density of cotton bag is less than that of the iron bar, so the volume of cotton bag is more compared to iron bar. So the cotton bag experiences more upthrust due to the presence of air. Actual weight = Measured Weight + Buoyant Force

### Exercise 6

•  Q1 How does the force of gravitation between two objects change when the distance between them is reduced to half ? Ans: We know that the universal law of gravitation,  gravitational force acting between two objects is inversely proportional to the square of the distance (r) between them, i.e., If distance r becomes r/2, then the gravitational force will be proportional to When the distance is reduced to half the gravitational force becomes four times larger than the previous value. Q2 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: 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 force is directly proportional to mass, acceleration is constant for a body of any mass. Hence, heavy objects do not fall faster than light objects. Q3 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.) Ans: Given; Mass of Earth, M = 6 × 1024 kg Mass of object, m = 1 kg Universal gravitational constant, G = 6.7 × 10−11 Nm2 kg−2 radius of the Earth (R) = R = 6.4 × 106 m Gravitational force,  Q4 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? Ans: The Earth attracts the moon with an equal force with which the moon attracts the earth but these forces are in opposite directions. According to universal law of gravitation, Where, m1m2 is mass of earth and the moon respectively and r is distance between the earth and the moon. Q5 If the moon attracts the earth, why does the earth not move towards the moon? Ans: Apply Newton’s third law which states that every action has an equal and opposite reaction. Therefore, the Earth and the moon experience the same amount of gravitational forces from each other. Both bodies revolve around their common centre of mass and centrifugal force balances the gravitational force. However, the mass of the Earth is much larger than the mass of the moon.  For this reason, the Earth does not move towards the moon. Q6 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: According to the universal law of gravitation, (i) Force is directly proportional to the masses of the objects. If the mass of one object is doubled, then the gravitational force will also get doubled. (ii) Force is inversely proportional to the square of the distances between the objects. If the distance is doubled, then the gravitational force becomes one-fourth. Similarly, if the distance is tripled, then the gravitational force becomes one-ninth. (iii) Force is directly proportional to the product of masses of the objects. If the masses of both the objects are doubled, then the gravitational force becomes four times. Q7 What is the importance of universal law of gravitation? Ans: The importance of universal law of gravitation ; 1. It helps us bind together with the Earth. 2. A body which goes up will not come down if there is no gravitational force. Q8 What is the acceleration of free fall? Ans: When the body falls due to Earth’s gravitational pull, its velocity changes and is said to be accelerated due to Earth’s gravity and it falls freely called free fall. Acceleration of free fall is 9.8 ms−2, which is constant for all objects. Q9 What do we call the gravitational force between the earth and an object? Ans: Gravitational force between the earth and an object is called the weight of the object. Q10 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.] Ans: Weight of an object on the Earth is given by: W = mg Where, m = Mass of the object g = Acceleration due to gravity Since the acceleration due to gravity is less at the equator as compared to that at poles, the weight of the gold will be less at the equator than at the poles. Hence, Amit’s friend will not agree with the weight of the gold bought. Q11 Why will a sheet of paper fall slower than one that is crumpled into a ball? Ans: A sheet of paper will fall slower than one that is crumpled into a ball because of the different drag force. Crumpled ball has a smaller surface area so the resistance offered by air is less than in the case of a sheet of paper which has a larger surface area. Q12 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? Ans: Given; gravitational force on surface of the moon = 1/6 x gravitational force on surface of the Earth Also, Weight = Mass × Acceleration Mass of the object = 10 kg Acceleration due to gravity, g = 9.8 m/s2 Therefore, weight of  object on the Earth = 10 × 9.8 = 98 N And, weight of the same object on the moon = 98 / 6 = 16.33 N Q13 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. Ans: We know that the equation of motion under gravity: v2 − u2 = 2 gs Where, u = Initial velocity of the ball v = Final velocity of the ball s = Height achieved by the ball g = Acceleration due to gravity At maximum height, final velocity of the ball is zero, i.e., v = 0 u = 49 m/s During upward motion, g = − 9.8 m s−2 (i) Let; h = the maximum height attained by the ball. Hence, (ii) Let; t = time taken by the ball to reach the height 122.5 m  then using the equation of motion: v = u + gt We get, But, Time of ascent = Time of descent Therefore, total time taken by the ball to return = 5 + 5 = 10 s Q14 A stone is released from the top of a tower of height 19.6 m. Calculate its final velocity. Ans: Initial velocity of the stone = u = 0  Final velocity of the stone = v  Height of the stone = s = 19.6 m  Acceleration due to gravity = g = 9.8 m s−2 According to the equation of motion under gravity: v2 − u2 = 2 gs v2 − 02 = 2 × 9.8 × 19.6 v2 = 2 × 9.8 × 19.6 = (19.6)2 v = 19.6 m s−1 Hence, the velocity of the stone just before touching the ground is 19.6 m s−1. Q15 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? Ans: Initial velocity of the stone = u = 40 m/s  Final velocity of the stone = v = 0  Height of the stone = s  Acceleration due to gravity = g = −10 m s−2 Let h = maximum height attained by the stone. According to the equation of motion under gravity: v2 − u2 = 2 gs Therefore, total distance covered by the stone during its upward and downward journey = 80 + 80 = 160 m Net displacement of the stone during its upward and downward journey = 80 + (−80) = 0 Q16 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. Ans: MSun = Mass of the Sun = 2 × 1030 kg MEarth = Mass of the Earth = 6 × 1024 kg R = Average distance between the Earth and the Sun = 1.5 × 1011 m G = Universal gravitational constant = 6.7 × 10−11 Nm2 kg−2 Force of gravitation = F =  Q17 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. Ans: Let the two stones meet after a time t. (i) For the stone dropped from the tower: Initial velocity, u = 0 m/s Let the displacement = s Acceleration due to gravity, g = 9.8 m s−2 From the equation of motion, ...(1) (ii) For the stone thrown upwards: Initial velocity, u = 25 m/s Let the displacement = s'. Acceleration due to gravity, g = −9.8 m s−2 Equation of motion, ...(2) The combined displacement is ; In 4 s, the falling stone has covered a distance given by equation (1) as Therefore, the stones will meet after 4 s and the distance is 80 m from the top. Q18 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. Ans: The ball takes a total of 6 s for its upward and downward journey. Time taken to reach maximum height = 6 / 2 = 3 s Hence, it has taken 3 s to attain the maximum height (a) Let initial velocity = u m/s Final velocity of the ball at the maximum height, v = 0 m/s Acceleration due to gravity, g = −9.8 m s−2 Equation of motion v = u + gt  0 = u + (−9.8 × 3) u = 9.8 × 3 = 29.4 ms−1 Hence, the ball was thrown upwards with a velocity of 29.4 m s−1. (b) Let the maximum height attained by the ball = h Initial velocity during the upward journey, u = 29.4 m/s Final velocity, v = 0 m/s Acceleration due to gravity, g = −9.8 m s−2 From the equation of motion,  (c) Ball attains the maximum height after 3 s. After attaining this height, it will start falling downwards. In this case, Initial velocity, u = 0 m/s Position of the ball after 4 s of the throw is given by the distance travelled by it during its downward journey in 4 s − 3 s = 1 s. Equation of motion, s = 0 x 1 + ½ x 9.8 x 12 s = 4.9 m  Total height = 44.1 m This means that the ball is 39.2 m (44.1 m − 4.9 m) above the ground after 4 seconds. Q19 In what direction does the buoyant force on an object immersed in a liquid act? Ans: The buoyant force acts in the upward direction on the object which is immersed in a liquid. Q20 Why does a block of plastic released under water come up to the surface of water? Ans: When a plastic is immersed in water, there are two forces acting upon it. One is the gravitational force, which pulls the object downwards, and the other is the buoyant force, which pushes the object upwards. In this case, the buoyant force on plastic is more than the gravitational force. Thus, the plastic will come up to the surface of water. Q21 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? Ans: An object sinks in liquid when its density is greater than the liquid. On the other hand, an object floats on liquid when its density is less than the liquid. Here, density of the substance = The density of the substance is more than the density of water (1 g cm−3). Hence, the substance will sink in water. Q22 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 cm-3? What will be the mass of the water displaced by this packet? Ans: Density of the 500 g sealed packet Density of packet > density of water  Hence, it will sink in water. Mass of water displaced by packet = Volume of the packet = 350 g The mass of water displaced is 350 g.

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