NCERT Exemplar Solutions Class 9 Science Gravitation

Question 6:  In the relation F = GMm/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 universal constant of nature

Answer 6:   (d) is universal constant of nature. 

The quantity G is a natural universal constant. It is applicable to all living things in the world. In Newton's universal law of gravitation, it is the proportionality constant.

G is 6.67x 1CT^-11 Nm² kg^-2, which is the accepted value.

Question 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

Answer 7:   (c) any two bodies having some mass.

where,              F = Force of attraction between the two bodies

              m₁ m₂   = Mass of two bodies

                         G = Gravitational Constant

                          r = Distance between the two bodies

Question 8:  The value of quantity G in the law of gravitation
(a) depends on mass of the earth only
(b) depends on radius of earth only
(c) depends on both mass and radius of the earth
(d) is independent of mass and radius of the earth

Answer 8:   (d) is independent of mass and radius of the earth.

G, also known as the universal gravitational constant, is a proportionality constant. It is unaffected by the earth's mass or radius.

Question 9:  Two particles are placed at some distance. If the mass of each of the two particle is doubled, keeping the distance between them unchanged, the value of gravitational force between them will be

(a) 14 times

(b) 4 times

(c) 12 times

(d) unchanged

Answer 9:   (b) 4 times.

We know that, according to gravitational force

Question 10:  The atmosphere is held to the earth by

(a) gravity                                                 

(b) wind

(c) clouds                                                   

(d) earth’s magnetic field

Answer 10:   (a) gravity. 

Gravity binds the atmosphere to the surface.

Question 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

Answer 11:   (d) universal.

We know that, the gravitational force,

As a result, the universal gravitational constant is the force of attraction between two unit point masses separated by a unit distance.

Question 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

Answer 12:  (a) zero. 

The weight of an object, w = mg
At the centre of the earth, acceleration due to gravity g is zero. And is given by

where h = distance from surface of the earth to centre of the earth and at
centre (h = R) i.e., g’=0.
So, w = m x 0 = 0

Question 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) 2N       

(b) 8N                         

(c) 10N                    

(d) 12N

Answer 13:   (a) 2N.

Given, Weight of an object in air = 10N

             Weight of an object in water = 8N
So, the weight of the liquid displaced by the object F = 10 - 8 =2N, and we know that buoyancy force = weight of the liquid displaced by the body, according to Archimedes' Theory.

Question 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

Answer 14:  (b) maximum when breadth and width form the base. 

Now, when the base is shaped by breadth and width, according to the query. The amount of space available would be minimal. As a result, the strain would be at its peak.

Question 15:  An apple falls from a tree because of gravitational attraction between the earth and apple. If 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

Answer 15:   (d) F₁ and F₂ are equal.

According to Newton’s universal law of gravitation, force exerted by the one body to other body is equal in magnitude and given by

Short Answer Type Questions...........................

Question 16:  What is the source of centripetal force that a planet requires to revolve around the sun? On what factors does that force depend? 

Answer 16:   The centripetal force is responsible for the planet's rotation around the earth. The gravitational force between the earth and the sun produces this centripetal force. 

This force is proportional to the mass of the sun and the mass of the earth, as well as the distance between them. 

Question 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?

Answer 17:

Time taken by both stone is given by second equation of motion s = ut +1/2 at²
As,     u_y = 0, so, s = 1/2at²
and here                                              s = h
Where, m = Initial velocity in y-axis
a = g acceleration due to gravity
t = time displacement to time

 

As a result, if we drop a stone from a height (h) while simultaneously throwing another stone in a horizontal direction, both stones would hit simultaneously the earth at different locations.  

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

Answer 18:    The moon goes off in a straight line because the earth's gravity is absent. A tangent to the circular path would be this straight line.

Question 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 same time to reach the surface of earth. Justify your answer.

Answer 19:   No, such packets do not take the same amount of time to hit the earth's surface. Due to the rotation of the planet, the value of g (i.e., gravity acceleration) differs at the poles and equator, and is given by g'= g -a>2rsin0, with 0 = 0 at the poles and 0 = 90° at the equator.

So, value of g at equator is less than value of g at poles and we know that,

Due to the fact that g is greater at the poles than at the equator. As a result, a packet dropped over the north pole would be the first to hit the earth's surface.

Question 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?

Answer 20:
Weight of person on moon = 1/6^th of weight on earth

Therefore, ‘g’ on moon = 1/6th ‘g’ on earth

The force that is applied by the man to lift mass ‘m’ is

F = mg = 15kg    (on earth)

If he can lift a certain mass ‘m’ by applying the same force on moon, then

F = 15 * 6 = 90kg

This shows that the acceleration due to gravity on the moon is one-sixth that on Earth. As a result, on the moon, an individual can lift a mass that is six times heavier than on Earth.

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

Answer 21:

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

Answer 22:   The sun is the centre of the universe, and the world revolves around it. The world needs the centripetal force to revolve around the sun. The gravitational force between the sun and the earth provides this centripetal force. This gravitational force prevents the earth from colliding with the sun. 

Long Answer Type Questions......................

Question 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? 

Answer 23:  Let R and M be the radius and mass of the earth 

Then 

Weight of the object = M/R² 

Original weight W₀ = mg = mg M/R² 

Hypothetically 4m and R becomes R/2 

Then, weight = mG 4M /(R/2) ² 

= (16m g) M/R² 

= 10xW₀ 

Weight will be 16 times. 

Question 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. 

Answer 24:   Newton's universal law of gravitation describes the force of attraction between two bodies of mass m₁ and m₂ and separated by a distance r

(where M = Mass of the earth, R = Radius of the earth)
And it's obvious from the equation that gravity's acceleration (g) is solely determined by the earth's mass and radius. As a result, under the influence of gravity, two bricks bound together would not fall faster than a single brick. As a consequence, the hypothesis is false. 

Question 25:  Two objects of masses m₁ and m₂ having the same size are dropped simultaneously from heights /7_a and 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 reason. 

Answer 25:

Question 26:  (i) 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 reason for each case.
(ii) A ball weighing 4 kg of density 4000 kgm−³ is completely immersed in water of density 10³ kgm−³. Find the force of buoyancy on it. (Given, g= 10 ms⁻²)

Answer 26:

i)        Buoyant force, F = Vpg
(where, p= Density of water, V = Volume of water displaced by the body)
Since saturated salt solutions have a higher density than water, buoyant force is determined by volume and density. As a result, in a saturated solution, the buoyant force on the cube would be greater.
If each side of the cube is cut down to 4 cm, the volume of the cube is reduced. Since buoyant force is proportional to volume. As a result, the buoyant force would be lower than in the first case for water.

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] 

    ∴                                Volume of solid =  (Mass )/Density

                                                                = 4/4000 = 1/1000 m³ 

           Buoyancy,                                          F = Vρg

                                                               = 1/1000 × 1000 × 10 = 10 N