NCERT Exemplar Problems Class 9 Science – Gravitation
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 same magnitude
(d) undergo a change in their inertia
(a) Objects of different masses falling freely near the surface of the moon would have the same velocities at any instant because they will have same acceleration due to gravity.
The value of acceleration due to gravity
(a) is same on equator and poles
(b) is least on poles
(c) is least on equator
(d) increases from pole to equator
(c) It is least at the equator and maximum at the poles due to rotation of earth
i.e., it is given by
g’=g-co2 R sin0
At poles 0 = 0, So g maximum
At equator 0 = 90°, So g maximum
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 boy is whirling a stone tied with a string in an 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
(c) In circular motion, the direction of velocity at a point is always along the tangent at that point. If string breaks, then the centripetal force acting on the stone becomes zero and it will move along a straight line tangential to the circular path.
(a) d, >d2> d3 (b) d, > d2 < d3
(c) d, < d2 > d3 (d) d, < d2 < d3
(d) In a liquid of higher density more part of the object remains outside the liquid. Since, the order of part of their volume outside the liquid is given by (part of the body out side the liquid) ∞ densities of liquid
Thus, the order of densities in increasing order is
d1<d2< d 3
In the relation F = GMm/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 universal constant of nature
(d) The quantity G is universal constant of nature. It is applied to all the body present in universe It is constant of proportionality in Newton’s universal law of gravitation.
The accepted value of G is 6.67x 1CT-11 Nm2 kg-2.
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
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
G is the constant of proportionality and is called the universal gravitational constant. It is independent of mass and radius of the earth.
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
The atmosphere is held to the earth by
(a) gravity (b) wind
(c) clouds (d) earth’s magnetic field
(a) The atmosphere is held to the earth by gravity.
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
(d) We know that, the gravitational force,
Therefore, the force of attraction between two unit point masses separated by a unit distance is called universal gravitational constant.
The weight of an object at the centre of the earth of radius R, is
(c) R times the weight at the surface of the earth
(d) 1/R2 times the weight at the surface of the earth
(a) 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
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
(a) 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 according to Archimedes’ Principle, buoyancy force = weight of the liquid displaced by the body.
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
(b) Now, according to question, when base is formed by breadth and width. Area will be minimum. And so, pressure will be maximum.
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) F, is very much greater than F2 (b) F2 is very much greater than F,
(c) F, is only a little greater than F2 (d) F, and F2 are equal
Short Answer Type Questions
What is the source of centripetal force that a planet requires to revolve around the sun? On what factors does that force depend?
The motion of the planet around the earth is due to the centripetal force. This centripetal force is provided by the gravitational force between the planet and the sun.
This force depends on the mass of the sun and mass of the planet, and on the distance between sun and planet.
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?
Time taken by both stone is given by second equation of motion s = ut +1/2 at2
As, uy = 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
Therefore,- if we drop down a stone from a height (h) and at same time throw another stone in horizontal direction, then both the stone strike the earth simultaneously at different places.
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?
In the absence of gravity of earth, the moon flies off along a straight line. This straight line will be a tangent to the circular path.
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 same time to reach the surface of earth. Justify your answer.
No, those packets do not take same time to reach the surface of the earth. Because the value of g (i.e., acceleration due to gravity is) different at poles and equator due to rotation of the earth and is given by g’= g -a>2rsin0 and at poles 0 = 0 whereas at equator 0 = 90°.
Since, g is greatest at the poles than at the equator. So, packet dropped above the north pole will reach first at the surface of the earth.
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?
On earth Force applied by the man (F) on earth = m×g (m=mass)
= 90 kg As Mass does not change at every place. It is a concerned quantity. So, 15 kg will be maximum mass which can be lifted by the same force applied by the person on the moon.
Calculate the average density of the earth in terms of g, G and R.
The earth is acted upon by gravitation of the sun, even though it does not fall into the sun. Why?
The earth revolves around the sun. The centripetal force is needed by the earth to revolve around the sun. This centripetal force is provided by the gravitational force between the sun and the earth. And this gravitational force restricts the earth to fall into the sun.
Long Answer Type Questions
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?
Let radius and mass of the earth be R,M respectively and mass of an object be m.
Weight of the object,
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.
The force of attraction between two bodies of masses m, and m2 and separated by distance r is given by Newton’s universal law of gravitation
(where M = Mass of the earth, Ft = Radius of the earth)
And from the equation it is clear that, acceleration due to gravity (i.e., g) depends only on mass of the earth, the radius of the earth. So, two bricks tied together will not fall faster than a single bricks under the action of gravity. Hence, the hypothesis is not correct.
Two objects of masses m1 and m2 having the same size are dropped simultaneously from heights /7a 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.
(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)
(i) Buoyant force, F = Vpg
(where, p= Density of water, V = Volume of water displaced by the body)
Buoyant force depends upon volume and density, since, saturated salt solution have higher density than the water. So, in saturated solution, cube will experience a greater buoyant force. .
If each side of the cube is reduced to 4 cm, then the volume of cube become less. As buoyant force is directly proportional to the volume. So, buoyant force will be less than as compared to 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]