Gravitation

Multiple Choice Questions (MCQs)

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 same magnitude (d) undergo a change in their inertia
Ans. (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.
2. 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
Ans. (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 − ω2R sinθ
At poles θ = 0, So g maximum
At equator θ = 900 , So g maximum

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) F/4 (b) F/2 (c) F (d) 2F
Thinking Process
Gm1m2
Firstly, we use the Newton's universal law of gravitation i.e.,, F = , further we put given condition
r2
m m
i.e., m1' = 1 and m'2 = 2 in gravitational formula to get required new force.
2 2
Ans. (a)
We know that, according to force of gravitation
Gm1m2
F= (G= Gravitational constant)
r2
where m1 and m2 are the masses of two objects respectively. And r is the distance between the two
masses
Now, according to the question, if masses of both objects are halved,
m m
i.e., m1' = 1 and m'2 = 2
2 2
 m  m 
' ' G  1  2 
Gm1m2 2  2 
New force P= 2
= 
r r2
1 Gm1m2 F Gm1m2
= 2
= where =F
4 r 4 r2
F
So, new force F' =
4
1
Thus, the new gravitational force will become times of its original gravitational force.
4
4. 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
Ans. (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.

where vA, vB, vC, vD are the vertices point A, B, C, D in circular path.
1 2 3
5. An object is put one by one in three liquids having different densities. The object floats with , and
9 11 7
parts of their volumes outside the liquid surface in liquids of densities d1, d2 and d3, respectively. Which
of the following statement is correct?
(a) d1 > d2 > d3 (b) d1 > d2 < d3 (c) d1 < d2 > d3 (d) d1 < d2 < d3
Ans. (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 outside the liquid)  densities of liquid
1 2 3
 
9 11 7
Thus, the order of densities in increasing order is
d1  d2  d3
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
Ans. (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 6.67  10–11 Nm2 kg–2.
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)
Law of gravitation is applicable to all bodies having some mass. And is given by
Gm1m2
F=
r2
where, F = Force of attraction between the two bodies
 m1 ,m2 = Mass of two bodies
G = Gravitational constant
r = Distance between the two bodies.
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
Ans. (d)
G is the constant of proportionality and is called the universal gravitational constant. It is independent
of mass and radius of the earth.
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
1 1
(a) times (b) 4 times (c) times (d) unchanged
4 2
Thinking Process
GMm
Firstly, we use the Newton's universal law of gravitation i.e., F = 2 , further we put given condition i.e.,
r
M=2M and m=2m in Newton's gravitational formula to get required new force.
Ans. (b)
We know that, according to gravitational force
Mm
F=G 2
r
where, F = Force between two mass
M = First mass
m = Second mass
G = Gravitational constant
r = Distant between two mass
According to the question,
F’ = New force when mass is doubled
If mass of each particle is doubled
i.e., M = 2M and m = 2m
These value put in Eq. (i), we get

F' = G
(2M )(2m )
r2
Mm
F' = 4G
r
From Eq. (i), F'=4F
10. The atmosphere is held to the earth by
(a) gravity (b) wind (c) clouds (d) earth's magnetic field
Ans. (a)
The atmosphere is held to the earth by 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)
We know that, the gravitational force,
 Mm
F=G
r2

Where, F = Force between mass

m = Mass of the body
M = Gravitational Constant
r = Distant between two mass
Given, M =1 unit, m = 1 unit and r = 1 unit, we get
11
F=G 2  F=G
(1 )
Therefore, the force of attraction between two unit point masses separated by a unit distance is called
universal gravitational constant.
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)
The weight of an object, w = mg
 h
At the centre of the earth, acceleration due to gravity g is zero. And is given by g' = g  1 −  , where
 R
h = distance from surface of the earth to centre of the earth and at centre(h = R) i.e., g'= 0.
So, w=m  0=0
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
Thinking Process
Loss in weight of the object when dipped in a liquid is equal to the buoyancy force.
Ans. (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.
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
Thinking Process
Thrust Force
As we know that Pressure = = . Pressure exerted by the brick will be maximum when area is
Area Area
small.
Ans. (b)
 Now, according to question, when base is formed by breadth and width. Area will be minimum. And so,
pressure will be maximum.
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)
According to Newton's universal law of gravitation, force exerted by the one body to other body is equal
 Gm1m2 
in magnitude and given by  F = and opposite in direction.
 r2 
16. Two persons weighing 50 kg and 60 kg are seated across a table. If they are one metre apart, the
gravitational force between them is:
(a) 5 × 10–7N
(b) 2 × 10–7N
(c) 4 × 10–7N
(d) 3 × 10–7N
Ans:(b)
6.67 10−11  50 60
F= (1)2
= 6.67 × 3 × 10–8
= 20.01 × 10–8 N
= 2.001 × 10–7 N.
17. The universal constant of gravitation G has the units :
(a) N
(b) m/s2
(c) Nm 2 kg – 2
(a) J
Ans: (c)
18. A coin and a feather are dropped together in a vacuum. Then :
(a) the coin will reach the ground first
(b) the feather will reach the ground first
(c) both will reach the ground at the same time
(d) the feather will not fall down
Ans: (c)
19. A balloon of mass ‘m’ is rising with an acceleration ‘a’. A fraction of its mass is detached from the
balloon.
Its acceleration will :
(a) decrease
(b) increase
(c) remain the same
(d) none of these
Ans: (b)
Suppose upthrust = Reaction = R
R = m (g + a)
if mass m1 is detached
 R = (m–m1) g+(m–m1)2a
m (g + a) = (m–m1) g + (m–m1)2a
= (m–m1) (g + 2a)
m( g + a )
 m1 =
g + 2a
20. The gravitational pull exerted by the earth on a body is called :
(a) true weight
(b) gravitational mass
(c) apparent weight
(d) inertial mass
Ans: (a)