NCERT Exemplar: Gravitation | Science Class 9 PDF Download

Multiple Choice Questions

Q.1. Two objects of different masses falling freely near the surface of the moon would 
(a) have the same velocities at any instant 
(b) have different accelerations 
(c) experience forces of the same magnitude 
(d) undergo a change in their inertia 
Ans: (a)
Explanation:  The same acceleration due to gravity of the Moon is applied to both objects. In a free fall, velocity depends only on the acceleration produced by gravity. 

• The acceleration due to gravity is independent of the mass of the body.
• So, they will have the same velocities at any instant, irrespective of their masses.

Q.2. The value of acceleration due to gravity
(a) is the same on the equator and the poles
(b) is least on the poles
(c) is least on the equator
(d) increases from pole to equator
Ans: (c)
Explanation: The acceleration due to gravity is given by g=GM_E / R_E²​​​​ where G is the universal gravitational constant, M_E is the mass of the Earth, and R_E is the radius of the Earth. 

• Acceleration due to gravity is inversely proportional to the radius of the Earth.  
• At the equator, the radius of the Earth is maximum. Hence, the acceleration due to gravity is least at the equator.

Q.3. The gravitational force between two objects is F. If the masses of both objects are halved without changing the distance between them, then the gravitational force would become
(a) F/4
(b) F/2
(c) F
(d) 2 F
Ans: (a)

Explanation: 

• The gravitational force between two objects varies directly as their masses and inversely as the square of the distance between them. 
• So, when the masses of both objects are halved without changing the distance, the gravitational force between them would become one-fourth of the original value.

Q.4. A boy is whirling a stone tied with a string in a horizontal circular path. If the string breaks, the stone
(a) will continue to move in the circular path
(b) will move along a straight line towards the centre of the circular path
(c) will move along a straight line tangential to the circular path
(d) will move along a straight line perpendicular to the circular path away from the boy
Ans: (c)
Explanation: At any instant, an object in circular motion tends to move in a straight line due to inertia. The object keeps on moving due to centripetal force, and it moves along a straight line tangential to the circular path when the string breaks.

Q.5. An object is put one by one in three liquids having different densities. The object floats with 1/9 , 2/11 and 3/7 parts of their volumes outside the liquid surface in liquids of densities d₁, d₂ and d₃, respectively. Which of the following statements is correct?
(a) d1> d2> d3
(b) d1> d2< d3
(c) d1< d2> d3
(d) d1< d2< d3
Ans: (d) 

Explanation: 

• Buoyant Force is when a rigid object is submerged in a fluid (completely or partially), and an upward force exists on the object that is equal to the weight of the fluid that is displaced by the object.
• In this case, there are 3 liquids with varying densities. ( 9/1 = 0.11, 2/11 = 0.18 and 3/7 = 0.43) . These are the volumes outside of liquids of densities d₁, d₂ and d₃, respectively. This means that the buoyant force is maximum for d₃ and minimum for d₁. As the buoyant force is proportional to density, the densities of the liquids are in the order d₁<d₂<d₃.

Q.6. In the relation F = G M m / d², the quantity G
(a) depends on the value of g at the place of observation
(b) is used only when the Earth is one of the two masses
(c) is greatest at the surface of the Earth
(d) is a universal constant of nature
Ans: (d)
Explanation:  

• G is called Newton’s constant.  Value of G is 6.66x 10^-11 Nm²kg^-2.  
• G is the universal gravitational constant, which remains constant at all places in the universe. 
• G is equivalent to the force of attraction between two bodies of unit mass and unit distance apart.

Q.7. Law of gravitation gives the gravitational force between
(a) The Earth and a point mass only
(b) The Earth and the Sun only
(c) any two bodies having some mass
(d) two charged bodies only
Ans: (c)

Explanation: Newton's law of gravitation can be used to calculate the gravitational force that exists between any two bodies of a certain mass. The force of attraction between two bodies is inversely proportional to the square of the distance between them and directly proportional to the product of their masses.

Q.8. The value of quantity G in the law of gravitation
(a) depends on the mass of Earth only
(b) depends on the radius of Earth only
(c) depends on both the mass and the radius of Earth
(d) is independent of the mass and radius of the Earth
Ans: (d)
Explanation: G is a universal constant; hence, it is independent of the mass and radius of the Earth.

Q.9. Two particles are placed at some distance. If the mass of each of the two particles is doubled, keeping the distance between them unchanged, the value of the gravitational force between them will be
(a) 14 times
(b) 4 times
(c) 12 times
(d) unchanged
Ans: (b)

Explanation: The gravitational force is directly proportional to the product of the masses. Doubling both masses increases the force to four times its initial value.

Q.10. The atmosphere is held to the Earth by
(a) gravity
(b) wind
(c) clouds
(d) Earth’s magnetic field
Ans: (a)

Explanation: Due to gravity, everything is drawn toward the Earth.  In fact, the air encircling our planet is kept in place by gravity, and this protective layer of air is referred to as the atmosphere.

Q.11. The force of attraction between two unit point masses separated by a unit distance is called 
(a) gravitational potential 
(b) acceleration due to gravity 
(c) gravitational field 
(d) universal gravitational constant 
Ans: (d)
Explanation: The gravitational force is directly proportional to the product of the masses. Doubling both masses increases the force to four times its initial value.
 
Here, point masses are separated by a unit distance
Hence m₁, m₂ and r = 1
Hence F = G, which is a universal constant. Hence answer is the universal gravitational constant

Q.12. The weight of an object at the centre of the Earth of radius R is
(a) zero
(b) infinite
(c) R times the weight at the surface of the Earth
(d) 1/R² times the weight at the surface of the Earth
Ans: (a)
Explanation: At the centre of the Earth acceleration due to gravity is zero. Since weight is the product of mass and acceleration due to gravity. The weight of the object at the centre of the Earth will be zero.

Q.13. An object weighs 10 N in air. When immersed fully in water, it weighs only 8 N. The weight of the liquid displaced by the object will be 
(a) 2 N 
(b) 8 N 
(c) 10 N 
(d) 12 N 
Ans: (a)
Explanation: According to Archimedes' principle

 Weight of displaced liquid = weight of object in air- weight of object in liquid
= 10N - 8N
= 2N

Q.14. A girl stands on a box having 60 cm length, 40 cm breadth and 20 cm width in three ways. In which of the following cases, pressure exerted by the brick will be 
(a) maximum when length and breadth form the base 
(b) maximum when breadth and width form the base 
(c) maximum when width and length form the base 
(d) the same in all the above three cases 
Ans: (b)
Explanation: Surface area and pressure are inversely proportional to each other. Pressure will be maximum when the surface area is minimum. Hence, the answer is maximum when breadth and width form the base because the surface area is going to be minimum when breadth and width form the base. 

Length = 60cm, Breadth = 40cm, Width = 20cm

Area of the base formed by length and breadth = 60 × 40 = 2400 cm²
Area of the base formed by breadth and width = 40 × 20 = 800 cm²
Area of the base formed by width and length = 20 × 60 = 1200cm²

Q.15. An apple falls from a tree because of gravitational attraction between the earth and apple. If F₁ is the magnitude of force exerted by the earth on the apple and _F2 is the magnitude of force exerted by apple on earth, then 
(a) F₁ is very much greater than F₂
(b) F₂ is very much greater than F₁
(c) F₁ is only a little greater than F₂
(d) F₁ and F₂ are equal 
Ans: (d)
Explanation: Newton’s third law of motion states that for every action there is an equal and opposite reaction. Hence, F₁ and F₂ are equal.

Short Answer Questions

Q.16. What is the source of centripetal force that a planet requires to revolve around the Sun? On what factors does that force depend? 
Ans: The source of the centripetal force that allows a planet to revolve around the Sun is the gravitational force. This force is influenced by two main factors:

• The masses of the planet and the Sun.
• The distance between the planet and the Sun.

If the gravitational force were to become zero, the planet would no longer follow a circular path and would instead move away in a straight line.

Q.17. On the earth, a stone is thrown from a height in a direction parallel to the earth’s surface while another stone is simultaneously dropped from the same height. Which stone would reach the ground first and why? 
Ans: Both stones will reach the ground at the same time because:

• They are dropped from the same height.
• Their initial velocities are the same.
• Both are affected equally by gravity.

This means that regardless of the direction in which one stone is thrown, the time taken to fall to the ground remains unchanged.

Q.18. Suppose the gravity of Earth suddenly becomes zero, then in which direction will the moon begin to move if no other celestial body affects it? 
Ans: If the Earth's gravity were to suddenly become zero, the moon would begin to move in a straight line. Specifically:

• The moon would follow a tangent to its current circular path.
• This means it would not orbit the Earth anymore.
• Instead, it would continue in a uniform straight line indefinitely.

Q.19. Identical packets are dropped from two aeroplanes, one above the equator and the other above the north pole, both at height h. Assuming all conditions are identical, will those packets take the same time to reach the surface of Earth? Justify your answer. 
Ans: The acceleration due to gravity, g, varies across the Earth's surface. This variation is due to the Earth's shape:

• The Earth is flattened at the poles and bulges at the equator.
• As a result, g is highest at the poles and lowest at the equator.

When identical packets are dropped from two aeroplanes at height h:

• The packet dropped at the equator will experience a lower value of g.
• This means it will fall more slowly compared to the packet dropped at the poles.

Consequently, the packet from the equator will take longer to reach the Earth's surface than the one from the poles.

Q.20. The weight of any person on the moon is about 1/6 times that on Earth. He can lift a mass of 15 kg on Earth. What will be the maximum mass which can be lifted by the same force applied by the person on the moon?
Ans: The weight of a person on the moon is about 1/6 of their weight on Earth. If a person can lift a mass of 15 kg on Earth, we can calculate the maximum mass they can lift on the moon using the same force.

• The force exerted by the person on Earth is calculated as: F = mg (where g is the acceleration due to gravity).
• On Earth, this force is: F = 15 kg × g.
• On the moon, the acceleration due to gravity is 1/6 that of Earth, so g (moon) = g (Earth) / 6.
• Using the same force on the moon, we have: F = m (moon) × g (moon).
• Substituting the values, we find: m (moon) = 15 kg × 6 = 90 kg.

This means the person can lift a mass that is 6 times heavier on the moon than on Earth.

Q.21. Calculate the average density of the Earth in terms of g, G and R.
Ans: Acceleration due to gravity, g = GM /R², where R is the radius of the Earth.
Mass of the Earth, M = gR²/G
Density of Earth D= mass/volume
= gR²/G x Ve
= gR²/G x 4πR³/3
= 3g/4πGR

Q.22. The Earth is acted upon by the gravity of the Sun, even though it does not fall into the Sun. Why? 
Ans: The Sun exerts a gravitational pull on the Earth, but the Earth does not fall into the Sun due to a balance of forces:

• The Sun provides a centripetal force that keeps the Earth in orbit.
• The Earth generates a centrifugal force because of its motion.
• These two forces balance each other, preventing the Earth from falling into the Sun.

Long Answer Questions

Q.23. How does the weight of an object vary with respect to the mass and radius of the Earth? In a hypothetical case, if the diameter of the Earth becomes half of its present value and its mass becomes four times its present value, then how would the weight of any object on the surface of the Earth be affected?
Ans: Let R and M be the radius and mass of the Earth.
Then, the weight of an object is directly proportional to the mass of the Earth and inversely proportional to the square of the radius of the Earth. i.e. 

Weight of the object ∝ M/R²
Original weight W₀ = mg = mG M/R²
Hypothetically, M becomes 4M and R becomes R/2
Then, weight = mG 4M /(R/2) ²
= (16m G) M/R²
= 16xW₀
The weight will be 16 times.

Q.24. How does the force of attraction between the two bodies depend upon their masses and the distance between them? A student thought that two bricks tied together would fall faster than a single one under the action of gravity. Do you agree with his hypothesis or not? Comment.
Ans: The hypothesis is incorrect. The force of attraction between two masses separated by distance r is given by Newton's law of gravitation, where F = Gm₁m₂/R², where G is the gravitational constant and which is a universal constant.

• Gravitational force is directly proportional to the product of the masses of two bodies and inversely proportional to the square of the distance between them. 
• Objects released from the same height fall at the same speed regardless of their mass. This is due to acceleration due to gravity, g = GM/R², where M is the mass, R is the radius of the Earth. 
• This equation shows that acceleration due to gravity depends on the mass of the Earth and radius of the Earth. 
• Hence, two bricks tied together will not fall faster than a single one.

Q.25. Two objects of masses m₁ and m_2, having the same size, are dropped simultaneously from heights h₁ and h₂, respectively. Find out the ratio of time they would take to reach the ground. Will this ratio remain the same if (i) one of the objects is hollow and the other one is solid, and (ii) both of them are hollow, size remaining the same in each case? Give a reason.
Ans: 

We know that
v=u+at
Here v=0 and a=g
so 0=u+gt
u=−gt --- (i)
We also know
v²- u²=2as ---(ii)
Here v=0,u=−gt from eqn (i) and S=h₁ and taking t=t₁
putting all the above values in Eq. (ii)
g²t₁²=2gh₁
or h₁=1/2gt₁² ----(iii)
Similarly for S=h₂ and t=t₂
h₂=1/2gt₂² ----(iv)
Dividing eqn (iii) & (iv) we get,
t₁/t₂=√h₁/h₂
The ratio will not change in either case because acceleration remains the same. In the case of free-fall acceleration, it does not depend upon the mass and size of the body.

26. (a) A cube of side 5 cm is immersed in water and then in a saturated salt solution. In which case will it experience a greater buoyant force? If each side of the cube is reduced to 4 cm and then immersed in water, what will be the effect on the buoyant force experienced by the cube as compared to the first case for water? Give a reason for each case.
(b) A ball weighing 4 kg of density 4000 kg m^–3 is completely immersed in water of density 103 kg m^–3 Find the force of buoyancy on it. (Given g = 10 m s^–2)
Ans: (i) Buoyant force, F = Vpg
p = Density of water, V = Volume of water displaced by the body
Volume and density of an object decide its Buoyancy. Cube will experience a greater buoyancy in a saturated solution. If the cube is reduced to 4 cm on each side, the volume of the cube becomes less as the buoyancy will be reduced, as the buoyant force is directly proportional to volume.
(ii) The magnitude of the buoyant force given by F = Vpg
where V = Volume of body immersed in water or volume of water displaced, p = Density of liquid.
[∴ Given, mass of a ball = 4 kg, density = 4000 kgm^-3].
Hence Volume of solid = mass/density