Gravitation _Subtopic:Newton's Law of Gravitation MCQs*

Ruhul Amin Alig

Class 11 |

Physics

chapter 8

Gravitation

Subtopic:Newton's Law of Gravitation

Question: From NCERT Subtopic:Newton's Law of Gravitation Derived PYQ

If the distance between two masses is doubled, the gravitational attraction between them:

1. Is doubled

2. Becomes four times

3. Is reduced to half

4. Is reduced to a quarter

Answer ▽

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Question: From NCERT Subtopic:Newton's Law of Gravitation Derived PYQ

The gravitational force between two stones of mass 1 kg each separated by a distance of

1 metre in vacuum is

1. Zero

2. 6.675 $\times 10^{‐ 5} n e w t o n$

3. $6.675 \times 10^{‐ 11} n e w t o n$

4. $6.675 \times 10^{‐ 8} n e w t o n$

Answer ▽

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Question: From NCERT Subtopic:Newton's Law of Gravitation Derived PYQ

Two particles of equal mass go round a circle of radius R under the action of their mutual
gravitational attraction. The speed of each particle is

1. $ν = \frac{1}{2 R} \sqrt{\frac{1}{G m}}$

2. $ν = \sqrt{\frac{G m}{2 R}}$

3. $ν = \frac{1}{2} \sqrt{\frac{G m}{R}}$

4. $ν = \sqrt{\frac{4 G m}{R}}$

\sqrt{}

Answer ▽

Correct option is

$\frac{1}{2} \frac{G m}{R}$

Given,
Masses of the two particles are $m_{1} = m_{2} = m$
And radius of the two particles are $r_{1} = r_{2} = R$
So ,The Gravitational force of attraction between the particles $F = \frac{G \times m \times m}{R ^{2}} - - - - - - - - (1)$
Ans, centripital force $F = \frac{m \times v ^{2}}{R} - - - - - - (2)$
From given condition (1) and (2)
$\frac{G m m}{( 2 R ) ^{2}} = \frac{m v ^{2}}{R}$ ,
$v = \frac{G m}{4 R} = \frac{1}{2} \frac{G m}{R}$
So the speed of the each particle is $v = \frac{1}{2} \frac{G m}{R}$

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Question: From NCERT Subtopic:Newton's Law of Gravitation Derived PYQ

The earth (mass = $6 \times 10^{24} k g$ ) revolves round the sun with angular velocity

$2 \times 10^{‐ 7} r a d / s$ in a circular orbit of radius $1.5 \times 10^{8} k m$ . The force exerted by the sun on

the earth in Newtons, is

1. $18 \times 10^{25}$

2. Zero

3. $27 \times 10^{39}$

4. $36 \times 10^{21}$

Answer ▽

Force exerted by sun of earth $= M W 2 R$
given $M = 6 \times 10^{24} k g$
$W = 2 \times 10^{- 7}$ rad/s
$R = 1.5 \times 10^{8} k m$
$F = (6 \times 10^{24}) (2 \times 10^{- 7}) 2 (1.5 \times 10^{8} \times 10^{3})$
$= 36 \times 10^{21} N$
$Ans- 4th option correct$

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Question: From NCERT Subtopic:Newton's Law of Gravitation Derived PYQ

The gravitational force between two point masses $m_{1}$ and $m_{2}$ at separation r is given by $F = k \frac{m_{1} m_{2}}{r^{2}}$ The constant k

1. Depends on system of units only

2. Depends on medium between masses only

3. Depends on both 1 and 2

4. Is independent of both 1 and 2

Answer ▽

1 solution

The gravitational constant is a universal constant. It remains as it is in any condition.
It does not depend on any of the factors like the temperature, mass, distance between the masses.

Value of G is $6.67 \times 1 0^{- 11} N m^{2} k g^{- 2}$

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Question:   From NCERT Subtopic:Newton's Law of Gravitation  Derived PYQ Who among the following gave first the experimental value of G?
1. Cavendish
2. Copernicus
3. Brook Taylor
4. None of these

Answer ▽

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Question: From NCERT Subtopic:Newton's Law of Gravitation Derived PYQ

Mass M is divided into two parts xM and $(1 - x) M$ . For a given separation, the value of x

for which the gravitational attraction between the two pieces becomes maximum is

1. $\frac{1}{2}$

2. $\frac{3}{5}$

3. 1

4. 2

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Question: From NCERT Subtopic:Newton's Law of Gravitation Derived PYQ Two sphere of mass m and M are situated in air and the gravitational force between them
is F. The space around the masses is now filled with a liquid of specific gravity 3. The
gravitational force will now be

1. F

2. $\frac{F}{3}$

3. $\frac{F}{9}$

4. 3 F

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Question: From NCERT Subtopic:Newton's Law of Gravitation Derived PYQ Two identical solid copper spheres of radius R were placed in contact with each other. The gravitational attraction between them is proportional to:

1. $R^{2}$

2. $R$

3. $R^{4}$

4. $R^{5}$

Answer ▽

3 option

F = $\frac{G M M}{R^{2}}$
$= \frac{G (\frac{4}{3} π R^{3} ρ) (\frac{4}{3} π R^{3} ρ)}{R^{2}}$
$∴ F \propto R^{4}$

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Question: From NCERT Subtopic:Newton's Law of Gravitation Derived PYQ

A mass M is split into two parts, m and (M–m), which are then separated by a certain distance. What ratio of m/M maximizes the gravitational force between the two parts

(1) 1/3

(2) 1/2

(3) 1/4

(4) 1/5

Answer ▽

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Question: From NCERT Subtopic:Newton's Law of Gravitation Derived PYQ

Two spherical bodies of masses M and 5M and radii R and 2R are released in free space with initial separation between their centres equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body before collision is

(1)2.5 R

(2)4.5 R

(3)7.5 R

(4)1.5 R

Answer ▽

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Question: From NCERT Subtopic:Newton's Law of Gravitation Derived PYQ AIPMT - 2012

A spherical planet has a mass $M_{p}$ $M_{p}$ $M_{p}$ and diameter $D_{p}$ $D_{p}$ $D_{p}$ . A particle of mass m falling freely near the surface of this planet will experience acceleration due to gravity equal to:

1. $\frac{4 {GM}_{p} m}{{D_{p}}^{2}}$

2. $\frac{4 {GM}_{p}}{{D_{p}}^{2}}$

3. $\frac{{GM}_{p} m}{{D_{p}}^{2}}$

4. $\frac{{GM}_{p}}{{D_{p}}^{2}}$

Answer ▽

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Question: From NCERT Subtopic:Newton's Law of Gravitation Derived PYQ

Newton's law of gravitation is true for:
1. only uncharged particles.
2. only for planets.
3. only for heavenly bodies.
4. All the bodies.

Answer ▽

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Question: From NCERT Subtopic:Newton's Law of Gravitation Derived PYQ As observed from the earth, the sun appears to move in an approximately circular orbit. For the motion of another planet like mercury as observed from the earth, this would:
(a) be similarly true
(b) not be true because the force between the earth and mercury is not inverse square law
(c) not be true because the major gravitational force on mercury is due to the sun
(d) not be true because mercury is influenced by forces other than gravitational forces

Answer ▽

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Question: From NCERT Subtopic:Newton's Law of Gravitation Derived PYQ

Different points in the earth are at slightly different distances from the sun and hence experience different forces due to gravitation. For a rigid body, we know that if various forces act at various points in it, the resultant motion is as if a net force acts on the centre of mass causing translation and net torque at the centre of mass causing rotation around an axis through the CM. For the earth-sun system (approximating the earth as a uniform density sphere):
(a) the torque is zero
(b) the torque causes the earth to spin
(c) the rigid body result is not applicable since the earth is not even approximately a rigid body
(d) the torque causes the earth to move around the sun

Answer ▽

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Question: From NCERT Subtopic:Newton's Law of Gravitation Derived PYQ Choose the wrong option.
(a) Inertial mass is a measure of the difficulty of accelerating a body by an external force whereas the gravitational mass is relevant in determining the gravitational force on it by an external mass.
(b) That the gravitational mass and inertial mass are equal is an experimental result.
(c) That the acceleration due to gravity on the earth is the same for all bodies is due to the equality of gravitational mass and inertial mass.
(d) Gravitational mass of a particle-like proton can depend on the presence of neighbouring heavy objects but the inertial mass cannot.

Answer ▽

(d)
Key concept: Inertial mass: It is the mass of the material body, which measures its inertia.
Gravitational Mass: It is the mass of the material body, which determines the gravitational pull acting upon it.
According to the principle of equivalence, Gravitational mass of proton is equivalent to its inertial mass and is independent of presence of neighboring heavy objects.
Important point: Comparison between inertial and gravitational mass:
• Both are measured in the same units.
• Both are scalars.
• Both do not depend on the shape and state of the body.
• Inertial mass is measured by applying Newton’s second law of motion whereas gravitational mass is measured by applying Newton’s law of gravitation.
• Spring balance measures gravitational mass and inertial balance measure inertial mass.

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Question: From NCERT Subtopic:Newton's Law of Gravitation Derived PYQ

There have been suggestions that the value of the gravitational constant G becomes smaller when considered over a very large time period (in billions of years) in the future. If that happens, for our earth,
(a) nothing will change
(b) we will become hotter after billions of years
(c) we will be going around but not strictly in closed orbits
(d) after a sufficiently long time, we will leave the solar system

(1) (a, c)

(2) (a, d)

(3) (c, d)

(4) (a, b)

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Question: From NCERT Subtopic:Newton's Law of Gravitation Derived PYQ

Three equal masses of m kg each are fixed at the vertices of an equilateral triangle ABC. What is the force acting on a mass 2m placed at the centroid G of the triangle? Take AG = BG = CG = 1 m.

1. ${Gm}^{2} (\hat{i} + \hat{j})$

2. ${Gm}^{2} (\hat{i} - \hat{j})$

3. 0

4. $2 {Gm}^{2} (\hat{i} + \hat{j})$

Answer ▽

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Question: From NCERT Subtopic:Newton's Law of Gravitation Derived PYQ

Three equal masses of m kg each are fixed at the vertices of an equilateral triangle ABC. What is the force acting on a mass 2m placed at the centroid G of the triangle if the mass at the vertex A is doubled? Take AG = BG = CG = 1 m.

1. ${Gm}^{2} (\hat{i} + \hat{j})$

2. ${Gm}^{2} (\hat{i} - \hat{j})$

3. 0

4. $2 {Gm}^{2} \hat{j}$

Answer ▽

When mass at A is $2$ m, then gravitational force on mass $2 m$ at G due to mass $2 m$ at A is
$F_{1}^{'} = G \frac{2 m \times 2 m}{1 ^{2}} = 4 G m^{2}$ along GA
The resultant force on mass $2 m$ at G due to masses at A, B and C is
$F_{1} = (F_{2} sin 3 0^{o} + F_{3} sin 3 0^{o})$
$= 4 G m^{2} - (2 G m^{2} \times \frac{1}{2} + 2 G m^{2} \times \frac{1}{2})$
$= 2 G m^{2}$ along GA.

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Gravitation _Subtopic:Newton's Law of Gravitation MCQs*

If the distance between two masses is doubled, the gravitational attraction between them:

The gravitational force between two stones of mass 1 kg each separated by a distance of

Two particles of equal mass go round a circle of radius R under the action of their mutual
gravitational attraction. The speed of each particle is

$\frac{1}{2} \frac{G m}{R}$

Force exerted by sun of earth $= M W 2 R$
given $M = 6 \times 10^{24} k g$
$W = 2 \times 10^{- 7}$ rad/s
$R = 1.5 \times 10^{8} k m$
$F = (6 \times 10^{24}) (2 \times 10^{- 7}) 2 (1.5 \times 10^{8} \times 10^{3})$
$= 36 \times 10^{21} N$
$Ans- 4th option correct$

The gravitational constant is a universal constant. It remains as it is in any condition.
It does not depend on any of the factors like the temperature, mass, distance between the masses.

Value of G is $6.67 \times 1 0^{- 11} N m^{2} k g^{- 2}$

Question:   From NCERT Subtopic:Newton's Law of Gravitation  Derived PYQ Who among the following gave first the experimental value of G?
1. Cavendish
2. Copernicus
3. Brook Taylor
4. None of these

Question: From NCERT Subtopic:Newton's Law of Gravitation Derived PYQ Two sphere of mass m and M are situated in air and the gravitational force between them
is F. The space around the masses is now filled with a liquid of specific gravity 3. The
gravitational force will now be

Question: From NCERT Subtopic:Newton's Law of Gravitation Derived PYQ Two identical solid copper spheres of radius R were placed in contact with each other. The gravitational attraction between them is proportional to:

A mass M is split into two parts, m and (M–m), which are then separated by a certain distance. What ratio of m/M maximizes the gravitational force between the two parts

Question: From NCERT Subtopic:Newton's Law of Gravitation Derived PYQ

Two spherical bodies of masses M and 5M and radii R and 2R are released in free space with initial separation between their centres equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body before collision is

A spherical planet has a mass $M_{p}$ $M_{p}$ $M_{p}$ and diameter $D_{p}$ $D_{p}$ $D_{p}$ . A particle of mass m falling freely near the surface of this planet will experience acceleration due to gravity equal to:

Newton's law of gravitation is true for:
1. only uncharged particles.
2. only for planets.
3. only for heavenly bodies.
4. All the bodies.

Three equal masses of m kg each are fixed at the vertices of an equilateral triangle ABC. What is the force acting on a mass 2m placed at the centroid G of the triangle? Take AG = BG = CG = 1 m.

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Gravitation _Subtopic:Newton's Law of Gravitation MCQs*

If the distance between two masses is doubled, the gravitational attraction between them:

The gravitational force between two stones of mass 1 kg each separated by a distance of

Two particles of equal mass go round a circle of radius R under the action of their mutualgravitational attraction. The speed of each particle is

21​RGm​

Force exerted by sun of earth =MW2Rgiven M=6×1024kgW=2×10−7 rad/sR=1.5×108kmF=(6×1024)(2×10−7)2(1.5×108×103) =36×1021NAns- 4th option correct

The gravitational constant is a universal constant. It remains as it is in any condition. It does not depend on any of the factors like the temperature, mass, distance between the masses. Value of G is 6.67×10−11Nm2kg−2

Question: From NCERT Subtopic:Newton's Law of Gravitation Derived PYQ Who among the following gave first the experimental value of G?1. Cavendish 2. Copernicus3. Brook Taylor 4. None of these

Question: From NCERT Subtopic:Newton's Law of Gravitation Derived PYQ Two sphere of mass m and M are situated in air and the gravitational force between themis F. The space around the masses is now filled with a liquid of specific gravity 3. Thegravitational force will now be

Question: From NCERT Subtopic:Newton's Law of Gravitation Derived PYQ Two identical solid copper spheres of radius R were placed in contact with each other. The gravitational attraction between them is proportional to:

A mass M is split into two parts, m and (M–m), which are then separated by a certain distance. What ratio of m/M maximizes the gravitational force between the two parts

Question: From NCERT Subtopic:Newton's Law of Gravitation Derived PYQ

Two spherical bodies of masses M and 5M and radii R and 2R are released in free space with initial separation between their centres equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body before collision is

A spherical planet has a mass MpMp and diameter DpDp. A particle of mass m falling freely near the surface of this planet will experience acceleration due to gravity equal to:

Newton's law of gravitation is true for:1. only uncharged particles.2. only for planets.3. only for heavenly bodies.4. All the bodies.

Three equal masses of m kg each are fixed at the vertices of an equilateral triangle ABC. What is the force acting on a mass 2m placed at the centroid G of the triangle? Take AG = BG = CG = 1 m.

When mass at A is 2m, then gravitational force on mass 2m at G due to mass 2m at A isF1′​=G122m×2m​=4Gm2 along GAThe resultant force on mass 2m at G due to masses at A, B and C isF1​=(F2​sin30o+F3​sin30o)=4Gm2−(2Gm2×21​+2Gm2×21​)=2Gm2 along GA.

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Two particles of equal mass go round a circle of radius R under the action of their mutual
gravitational attraction. The speed of each particle is

$\frac{1}{2} \frac{G m}{R}$

Force exerted by sun of earth $= M W 2 R$
given $M = 6 \times 10^{24} k g$
$W = 2 \times 10^{- 7}$ rad/s
$R = 1.5 \times 10^{8} k m$
$F = (6 \times 10^{24}) (2 \times 10^{- 7}) 2 (1.5 \times 10^{8} \times 10^{3})$
$= 36 \times 10^{21} N$
$Ans- 4th option correct$

The gravitational constant is a universal constant. It remains as it is in any condition.
It does not depend on any of the factors like the temperature, mass, distance between the masses.

Value of G is $6.67 \times 1 0^{- 11} N m^{2} k g^{- 2}$

Question: From NCERT Subtopic:Newton's Law of Gravitation Derived PYQ Who among the following gave first the experimental value of G?
1. Cavendish
2. Copernicus
3. Brook Taylor
4. None of these

Question: From NCERT Subtopic:Newton's Law of Gravitation Derived PYQ Two sphere of mass m and M are situated in air and the gravitational force between them
is F. The space around the masses is now filled with a liquid of specific gravity 3. The
gravitational force will now be

A spherical planet has a mass $M_{p}$ $M_{p}$ $M_{p}$ and diameter $D_{p}$ $D_{p}$ $D_{p}$ . A particle of mass m falling freely near the surface of this planet will experience acceleration due to gravity equal to:

Newton's law of gravitation is true for:
1. only uncharged particles.
2. only for planets.
3. only for heavenly bodies.
4. All the bodies.