NCERT Exemplar for Class 9 Science Chapter 10 - Gravitation

Multiple Choice Questions

1. Two objects of different masses falling freely near the surface of moon would

(a) have 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) have same velocities at any instant

Explanation: The acceleration of an object in free fall is exclusively dictated by gravity's acceleration, and mass has no bearing. As a result, an object in free fall will have the same velocity at any given moment, regardless of its mass.

2. The value of acceleration due to gravity

(a) is same on equator and poles

(b) is least on poles

(c) is least on the equator

(d) increases from pole to equator

Ans: (c) is least on the equator

Explanation: The distance between the earth's surface and its centre is larger on the equator than at the poles. Furthermore, the square of the radius is inversely proportional to g. As a result, the gravitational acceleration at the equator is the least.

3. The gravitational force between two objects is F. If masses of both objects are halved without changing distance between them, then the gravitational force would become

(a) $\frac{F}{4}$

(b) $\frac{F}{2}$

(c) F

(d) 2F

Ans: (a) $\frac{F}{2}$

Explanation: The gravitational force between two things is equal to their masses and inversely proportional to the square of their distance. As a result, half the masses of both objects while keeping the same distance decreases the gravitational force between them to one-fourth of their original intensity.

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 center 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) will move along a straight line tangential to the circular path

Explanation: When an object moves in a circular pattern, it always moves in a rectilinear pattern. Due to the centripetal force, the item continues to travel on a circular route, but when the string breaks, the stone moves in a straight line tangential to the circular path.

5. An object is put one by one in three liquids having different densities. The object floats with $\frac{1}{9},\frac{2}{{11}}\;and\;\frac{3}{7}$ parts of their volumes of outside the liquid surface in liquids of densities d1, d2and 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) d1< d2< d3

Explanation: Let us find LCM of fractions of volumes outside the liquid surface in each

other.

$ = \frac{1}{9} = \frac{2}{{11}} = \frac{3}{7}$

LCM of the denominator is 693 and using this, the fractions can be written as follows: 

$\frac{{77}}{{693}} = \frac{{126}}{{693}} = \frac{{297}}{{693}}$

This shows that the fractions are in ascending order. The density of the liquid determines the upward force it exerts on the item. The force exerted on an object is related to its density.
As a result, the densities of liquids are presented in increasing order.

6. In the relation $F = GM\frac{m}{{{d^2}}}$  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) is a universal constant of nature

Explanation: G is known as a universal constant of nature given by newton. also known as a universal gravitational constant whose numerical value is G means the force of gravity on a particular extraterrestrial body.

7. Law of gravitation gives the gravitational force between

(a) the earth and a point mass only

(b) the earth and Sun only

(c) any two bodies having some mass

(d) two charged bodies only

Ans: (c) any two bodies having some mass

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 the earth only

(c) depends on both mass and radius of the earth

(d) is independent of mass and radius of the earth 

Ans: (d) is independent of mass and radius of the earth

Explanation: Because G is a universal constant, its value is independent of the earth's mass or radius.

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 gravitational force between them will be

(a)$\frac{1}{4}$  times

(b) 4 times

(c) $\frac{1}{2}$  times

(d) unchanged

Ans: (b) 4 times

Explanation: we know:

$F = G \times 2{m_1} \times \frac{{2{m_2}}}{{{r^2}}}$

$F = \;G \times {m_1} \times \frac{{2{m_2}}}{{{r^2}}}$

$F = 4 \times \;G \times {m_1} \times \frac{{2{m_2}}}{{{r^2}}}$

The gravitational force between two objects is proportional to their masses and inversely proportional to their distance squared. As a result, doubling the masses of both objects without changing their distance will result in a fourfold increase in gravitational force between them.

10. The atmosphere is held to the earth by

(a) gravity

(b) wind

(c) clouds

(d) earth’s magnetic field

Ans: (a) gravity

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) universal gravitational constant

Explanation: we know,

$F = \;G \times {m_1} \times \frac{{2{m_2}}}{{{r^2}}}$

Given: m1 = 1 unit, m2= 1unit, r= 1 unit

So, F= G(universal gravitational constant)

12. The weight of an object at the center of the earth of radius R is

(a) zero

(b) infinite

(c) R times the weight at the surface of the earth

(d) $\frac{1}{{{R^2}}}$ times the weight at surface of the earth

Ans: (a) zero

Explanation: At the core of the Earth, the acceleration due to gravity is zero. We already know that weight is a function of mass and g. As a result, when g = 0, weight is zero.

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) 2 N

Explanation: The weight of liquid displaced by an object is the weight in air minus the weight in liquid, which equals 10 N – 8 N = 2 N. Furthermore, when an item is immersed in water, its weight seems to be lowered by the same amount as the weight of liquid displaced by the object, according to Archimedes' hypothesis.

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) maximum when breadth and width form the base

Explanation: Pressure and surface area are inversely proportional. The pressure is highest when the surface area is the smallest. As a consequence, response (b) is the correct one.

15. An apple falls from a tree because of gravitational attraction between the earth and apple. If F1is the magnitude of force exerted by the earth on the apple and F2is 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) F1 and F2 are equal

Explanation: This is in accordance with Newton’s Third Law of Motion which states that for every action there is an equal and opposite reaction.

Short Answer Questions

16. What is the source of the centripetal force that a planet requires revolving around the Sun? On what factors does that force depend?

Ans: Centripetal force is necessary to move an object in a circular path. The gravitational pull of the sun provides the centripetal force in this condition. This force is determined by the mass of the sun and the planet, as well as the distance between them.

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 take the same amount of time to reach the bottom since they fall from the same height.

18. Suppose gravity of earth suddenly becomes zero, then in which direction will the moon begin to move if no other celestial body affects it?

Ans: Because the moon's circular motion is due to the centripetal force provided by the earth's gravitational force, and if gravitational force becomes zero, the moon will begin to move in a straight line in the direction it was moving at the time, the moon will begin to move in a straight line in the direction it was moving at the time. As a result, it will follow a straight line.

19. Identical packets are dropped from two airplanes, 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 the earth. Justify your answer.

Ans: The value of 'g' is smaller towards the equator than it is at the poles. As a result, near the equator, the package falls more slowly than at the poles. As a result, the package will linger in the air for longer when dropped at the equator.

20. The weight of any person on the moon is about 1/6 times that on the earth. He can lift a mass of 15 kg on the earth. What will be the maximum mass, which can be lifted by the same force applied by the person on the moon?

Ans: Because a person's weight on the moon is around one-sixth that of a person on Earth, the acceleration due to gravity on the moon is also one-sixth that of the Earth. This means that a human can lift six times as much weight on the moon as he can on Earth with the same power. As a result, the maximum mass that can be lifted using the same force as a person on the moon is 6 15 kg = 90 kg.

21. Calculate the average density of the earth in terms of g, G, and R.

Ans: We know,

$g = \frac{{GM}}{{{R^2}}}$

or

$D = \frac{{mass}}{{volume}}\; = \frac{{g \times {R^2}}}{{G \times V}}$

$M = \frac{{g \times {R^2}}}{G}$

(where is the volume of the earth, M is mass of the earth, R is radius of the earth,

G is universal gravitational constant)

Hence

$D = \frac{{g \times {R^2}}}{{G \times \frac{4}{3}\pi {R^3}}} = \frac{{3g}}{{4\pi GR}}$

22. The earth is acted upon by gravitation of the Sun, even though it does not fall into the Sun. Why?

Ans: The centripetal force necessary to keep the earth in orbit is supplied by the sun's gravitational force. The centrifugal force caused by the earth's rotation counteracts this. As a consequence, these pressures balance each other on a second-by-second basis, letting the earth remain in its orbit without colliding with the sun or drifting obliquely away from its circle.

Long Answer Questions

23. How does the weight of an object vary with respect to 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 of its present value, then how would the weight of any object on the surface of the earth be affected?

Ans: 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 a body=$\infty \frac{M}{{{R^2}}}$   

Original weight  

$W = mg = mG\;\frac{M}{{{R^2}}}$

When hypothetically M becomes 4 M and R becomes $\frac{R}{2}$

Then weight becomes

${W_n} = m{G_2}\frac{{4M}}{{\frac{R}{2}}} = \;\left( {16mG} \right)\frac{M}{{{R^2}}} = \;16 \times W$

The weight will become 16 times the present weight.

24. How does the force of attraction between the two bodies depend upon their masses and 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: (i) According to newton's law of attraction

Force of attraction between the two bodies is directly proportional to product of masses of

two bodies i.e

$F\; \propto {m_1}{m_2}$

And inversely proportional to square of the distance between the two bodies i.e

$F\; \propto \frac{1}{{{a^2}}}$

(ii) we know that $g = G\frac{M}{{{r^2}}}$

We may deduce from the preceding relationship that the value of g (gravitational acceleration) is independent of the mass of the falling body, hence in free-fall, the two bricks fall at the same speed and hit the ground at the same moment.
As a result, the hypothesis stated in the question is incorrect.

25. Two objects of masses m1and m2 having the same size are dropped simultaneously from heights h1and h2 respectively. Find out the ratio of time they would take in reaching 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                                                                                                          

we also know

v2-u2 = 2aS                                                                                                  -(ii)

Here v=0, u=-gt from eqn(i) and S=h1 and taking t=t1

putting all above values in eq (ii)

${h_2} = \frac{1}{2}g{t^2}$

or

${h_2} = \frac{1}{2}g{t^2}$                             - (iii)

Similarly for S=h2 and t=t2

${h_2} = \frac{1}{2}g{t^2}$                              -(iv)

Dividing eqn (iii) & (iv) we get,

 $\frac{{{t_1}}}{{{t_2}}} = \sqrt {\frac{{{h_1}}}{{{h_2}}}} $

The ratio will not change in either case because acceleration remains the same. In the case of free-fall acceleration does not depend upon mass and size of the body.

26. (a) A cube of side 5 cm is immersed in water and then in 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 the reason for each case.

Ans: (i) Because the density of the saturated salt solution is larger than that of water, the cube will feel a stronger buoyant force.

(ii)Because the smaller cube has a smaller volume than the original cube, it will have a lower buoyant force.

(b) A ball weight 4 kg of density 4000 kg m-3is completely immersed in water of density 103kg m-3. Find the force of buoyancy on it. (Given g = 10 ms^-2.)

Ans: Buoyant force = weight of the liquid displaced

= density of water × volume of water displaced × g

$1000 \times \frac{4}{{4000}} \times 10 = 10N$

The chapter 9 of class 9th syllabus provided by NCERT contains the concepts and fundamentals of gravitation. There are certain relevant concepts that are discussed in the chapter. The brief about these concepts is given below for student’s reference:

• Gravitation is a weak force but when large masses are involved it exerts a stronger force.

• Earth’s gravitational force is known as gravity.

• The force of earth’s gravity decreases as one moves from higher altitude to lower altitude.

• The force of earth’s gravity is also dependent on the surface of earth and thus decreases when one moves from equator to poles.

• The force with which earth attracts a body towards itself is dependent on the weight of the body.

• The weight of the body is defined as the product of mass of the body and acceleration due to gravity.

• The weight of an object may change from one place to another but the mass of the body remains the same.

• When immersed in a fluid, the object experiences a buoyant force acting on it.

• If the density of the object is lesser than the liquid in which it is immersed, then that object will float on the surface of the liquid.

• If the density of the object is greater than the liquid in which it is immersed, then that object will sink in the liquid.

Important concepts dealt with in Class 9 NCERT Exemplar for Chapter 10

The NCERT exemplar covers a large portion of the important topics present in chapter 10. The main focus is given to:

• Understanding Newton’s law of gravitation.

• Calculating the amount of force acting on two objects placed at a distance to each other.

• A vivid comparison between the gravitational force of the sun and earth acting on some specific object.

• Introduction to universal gravitational constant and its value.

• Comparison of acceleration due to gravity on earth and moon.