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Test: Universal Law of Gravitation - NEET MCQ


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25 Questions MCQ Test Physics Class 11 - Test: Universal Law of Gravitation

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Test: Universal Law of Gravitation - Question 1

The gravitational force between two objects each of mass m, separated by a distance r, is F. Gravitational force between two objects each of mass 2m separated by a distance 2r, will be

Detailed Solution for Test: Universal Law of Gravitation - Question 1

Gravitational force between two objects is mathematically represented as:
F = G × (m1×m2) / r2
Applying the Law of Gravitation,
Given that the initial force F is due to two objects each of mass m separated by a distance r.
Substituting these into the formula gives:
F = G × (m×m) / r2
The problem then states that the mass of each of the objects is doubled (to 2m) and the distance between them is also doubled (to 2r).
The new force F' using these values in the formula would be: F' = G × (2m×2m) / (2r)2

Simplifying this gives:
F' = 4G × (m×m) / 4×r2
This simplifies further to:
F' = G × (m×m) / r2
Comparing this with the original equation for F, we find that:
F' = F

Test: Universal Law of Gravitation - Question 2

Two bodies with same mass “m” separated by a distance “r” exert a gravitational force of F on each other. Suppose the distance between them is doubled and the force becomes F’. The ratio of two forces is

Detailed Solution for Test: Universal Law of Gravitation - Question 2

We know that the force of gravitation is inversely proportional to square of the distance between the two bodies,

i.e. F∝ r-2

Hence, when the distance between them will be doubled, the force will be reduced by 4 times

So, the ratio will be 4:1

Test: Universal Law of Gravitation - Question 3

The earth attracts the moon with a gravitational force of 1020 N. Then the moon attracts the earth with the gravitational force of

Detailed Solution for Test: Universal Law of Gravitation - Question 3

According to Newton's Third Law of Motion, every action has an equal and opposite reaction. This law applies to the gravitational forces between two bodies as well.

The gravitational force with which the Earth attracts the Moon is equal to the gravitational force with which the Moon attracts the Earth. This is because the forces are action and reaction pairs, as described by Newton's Third Law.

Therefore, if the Earth attracts the Moon with a gravitational force of 1020 N, then the Moon attracts the Earth with the same gravitational force of 1020 N.

Hence, the correct answer is b. 1020 N.

Test: Universal Law of Gravitation - Question 4

What is the force required to produce an acceleration of 9.8 m/s2 on a body of weight 9.8N? Take g = 9.8 m/s2.

Detailed Solution for Test: Universal Law of Gravitation - Question 4

Acceleration (a) = 9.8 m/s2

Weight of the body = 9.8 N

Since, Weight of the body = mg

⇒ Mass = Weight/g = 9.8/9.8 = 1 kg

We know that,

F = m × a

⇒ F = 1 kg × 9.8 m/s2

⇒ F = 9.8 Newton

Test: Universal Law of Gravitation - Question 5

The height at which the acceleration due to gravity becomes g/9 (where g = the acceleration due to gravity on the surface of the earth) in terms of R, the radius of the earth, is

Detailed Solution for Test: Universal Law of Gravitation - Question 5

Acceleration due to gravity at a height “h” is given by

g’ = g (R/R+h)2

Here,

g is the acceleration due to gravity on the surface

R is the radius of the earth

As g’ is given as g/9, we get

g/9 = g(R/R+h)2

⅓ = R/(R+h)

h=2R

Test: Universal Law of Gravitation - Question 6

Two isolated point masses m and M are separated by a distance l.  The moment of inertia of the system about an axis passing through a point where gravitational field is zero and perpendicular to the line joining the two masses, is  

Detailed Solution for Test: Universal Law of Gravitation - Question 6


Test: Universal Law of Gravitation - Question 7

The earth attracts the moon with a gravitational force of 1020 N. Then the moon attracts the earth with the gravitational force of  

Detailed Solution for Test: Universal Law of Gravitation - Question 7

The universal law of gravitation:

  • Sir Isaac Newton put forward the universal law of gravitation in 1687 and used it to explain the observed motions of the planets and moons.
  • The law states that every particle attracts every other particle in the universe with force directly proportional to the product of the masses and inversely proportional to the square of the distance between them.
  • Formula, Gravitational force,  where, F is the gravitational force between bodies, m1, and m2 are the masses of the bodies, d is the distance between the centers of two bodies, and G is the universal gravitational constant.
  • Here, universal gravitational constant, G = 6.67 × 10-11 Nm/kg2

  • The Universal Gravitational Law can explain almost anything, right from how an apple falls from a tree to why the moon revolves around the Earth.

Newton's third law of motion

  • It states that for every action, there is an equal and opposite reaction.
  • Action and reaction always act on two different bodies.

Explanation:

By Newton's Third Law and Newton's Law of Universal gravitation, the gravitational force the Earth exerts on the Moon is exactly the same as the force the Moon exerts on the Earth. 
F(Earth) = F(Moon)
Therefore, the moon attracts the earth with a gravitational force of 1020N.

Test: Universal Law of Gravitation - Question 8

The planet mercury is revolving in an elliptical orbit around Sun as shown.

The kinetic energy of mercury will be greatest at 

Detailed Solution for Test: Universal Law of Gravitation - Question 8

The kinetic energy of Mercury is related to its speed as it orbits the Sun. According to Kepler's laws:

  • Mercury moves faster when it is closer to the Sun.
  • This is due to the gravitational pull being stronger at closer distances.

Therefore, Mercury's kinetic energy is greatest at the point D in its orbit where it is nearest to the Sun, which is known as the perihelion.

Test: Universal Law of Gravitation - Question 9

Both earth and moon are subject to the gravitational force of the sun. As observed from the sun, the orbit of the moon

Detailed Solution for Test: Universal Law of Gravitation - Question 9

Concept:

Newton's law of gravitation: The force of attraction between any objects in the universe is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

  • The force acts along the line joining the two bodies.
  • The gravitational force is a central force that is It acts along the line joining the centers of two bodies.
  • It is a conservative force. This means that the work done by the gravitational force in displacing a body from one point to another is only dependent on the initial and final positions of the body and is independent of the path followed.


 

  • The moon revolves around the earth in a circular orbit (not perfectly circular). Sun exerts a gravitational force on both, the earth and moon. The major force acting on the moon is due to the gravitational force of attraction of the sun and earth and the moon is not always on the line joining the sun and earth. 
  • Two forces acting on the moon have different lines of action or the forces are not central, so it's motion will not be strictly elliptical.

Hence, option (b) is the correct answer.

Test: Universal Law of Gravitation - Question 10

The earth revolves round the sun in an elliptical orbit. Its speed is  

Detailed Solution for Test: Universal Law of Gravitation - Question 10

Conservation of angular momentum of the planet yields,

mv1r1 = mv2r⇒ v1 r1 = v2 r
∴ At closest distance, speed is maximum.

Test: Universal Law of Gravitation - Question 11

Two massive particles of masses M & m (M > m) are separated by a distance l. They rotate with equal angular velocity under their gravitational attraction.  The linear speed of the particle of mass m is

Detailed Solution for Test: Universal Law of Gravitation - Question 11

The system rotates about the centre of mass.  The gravitational force acting on the particle m accelerates it towards the centre of the circular path, which has the radius


Hence, (B) is correct. 

Test: Universal Law of Gravitation - Question 12

A particle is projected from the mid-point of the line joining two fixed particles each of mass m.  If the separation between the fixed particles is l, the minimum velocity of projection of the particle so as to escape is equal to

Detailed Solution for Test: Universal Law of Gravitation - Question 12

The gravitational potential at the mid-point  P,


⇒ The gravitational potential energy 

When it is projected with a speed v, it just escapes to infinity, and the potential & kinetic energy will become zero. 

Hence (D) is correct. 

Test: Universal Law of Gravitation - Question 13

The gravitational force on a body of mass m at a distance r from the centre of the Earth for r < R, where R is the radius of Earth, is proportional to:

Detailed Solution for Test: Universal Law of Gravitation - Question 13

We know, the gravitational force  
 

This is valid when R is the centre to centre distance between the two masses M and m.

At a distance r < R, the mass of Earth cannot be taken as M.

The new mass (M'):

The mass of earth will be contained for a radius r. Let us assume that the mean density of the earth is ρ and that earth is a sphere with a radius equal to the distance r. We know, mass = density × volume


Therefore the gravitational force, 

Hence the gravitational force, F ∝ r

Test: Universal Law of Gravitation - Question 14

Given below are two statements:

Statement-I: The law of gravitation holds good for any pair of bodies in the universe.
Statement-II: The weight of any person becomes zero when the person is at the center of the earth.

In the light of the above statements, choose the correct answer from the options given below:

Detailed Solution for Test: Universal Law of Gravitation - Question 14
  • Statement I: The law of gravitation holds good for any pair of bodies in the universe.

    • This statement is true.
    • Newton's law of universal gravitation applies to all objects in the universe, regardless of size or distance.
    • The force of attraction depends on the masses of the two objects and the distance between them.
  • Statement II: The weight of any person becomes zero when the person is at the center of the Earth.

    • This statement is also true.
    • At the center of the Earth, a person is equally attracted in all directions due to the surrounding mass.
    • As a result, the gravitational forces cancel out, effectively making the person's weight zero.
Test: Universal Law of Gravitation - Question 15

A planet has twice the density of earth but the acceleration due to gravity on its surface is exactly the same as on the surface of earth. Its radius in terms of radius of earth R will be  

Detailed Solution for Test: Universal Law of Gravitation - Question 15



Hence (B) is correct. 

Test: Universal Law of Gravitation - Question 16

A particle hanging from a spring stretches it by 1 cm at earth’s surface. Radius of earth is 6400 km. At a place 800 km above the earth’s surface, the same particle will stretch the spring by:  

Detailed Solution for Test: Universal Law of Gravitation - Question 16


Hence (D) is correct. 

Test: Universal Law of Gravitation - Question 17

A projectile is launched from the surface of the earth with a very high speed v at an angle θ with vertical. What is its velocity when it is at the farthest distance from the earth surface? Given that the maximum height reached by the projectile is equal to the height reached when it is launched perpendicular to earth with a velocity.

Detailed Solution for Test: Universal Law of Gravitation - Question 17

The maximum height reached by the projectile is given by


∴ h = R
Applying conservation of momentum 
mu' (R + h) = mv sin θ R

Test: Universal Law of Gravitation - Question 18

The mean radius of the earth is R, its angular speed about its own axis is ω and the acceleration due to gravity at the earth surface is g. The cube of radius of orbit of ‘geostationary satellite’ will be:

Detailed Solution for Test: Universal Law of Gravitation - Question 18



Hence, (D) is correct. 

Test: Universal Law of Gravitation - Question 19

Two particles of masses M and m are initially at rest and infinitely separated. When they move towards each other due to gravitational attraction, their relative velocity at any instant in terms of distance  ‘d’ between them at that instant is 

Detailed Solution for Test: Universal Law of Gravitation - Question 19

As the two particles moves in the influence of gravitational (conservative force) mechanical energy will be conserved.  
Let  p = momentum of mass m
So

Test: Universal Law of Gravitation - Question 20

The orbital velocity of an artificial satellite in a circular orbit just above earth’s surface is v0. For a satellite orbiting in a circular orbit at an altitude of half of earth’s radius is

Detailed Solution for Test: Universal Law of Gravitation - Question 20

Orbital velocity where R is radius of earth. 

*Answer can only contain numeric values
Test: Universal Law of Gravitation - Question 21

If the radius and density of a planet are two times and half respectively of those of earth, find the intensity of gravitational field at planet surface and escape velocity from planet.  


Detailed Solution for Test: Universal Law of Gravitation - Question 21

Acceleration due to gravity
Thus 
Escape velocity
∴ Escape velocity at planet 
= (√2) (11.2km / sec ) = 15.84 km/sec.

*Answer can only contain numeric values
Test: Universal Law of Gravitation - Question 22

A uniform sphere of mass M = 100 kg and a thin uniform rod of length l = 30cm and mass m = 300 kg oriented as shown in the figure. The distance of centre of sphere to the nearest end of the rod is r = 3 m. The gravitation force between them is given as x × 10–8 N. Find x
(G = 6.6 × 10–11 Nm2/kg2)


Detailed Solution for Test: Universal Law of Gravitation - Question 22


Since the sphere is uniform its entire mass may be considered to be concentrated at its centre. The force on the elementary mass dm is

But dm = m/l dx

*Answer can only contain numeric values
Test: Universal Law of Gravitation - Question 23

The distance between earth and moon is 4 × 105 km and the mass of earth is  81 times the mass of moon. Find the position (take 104 km as unit) of a point on the line joining the centres of earth and moon, where the gravitational field is zero.


Detailed Solution for Test: Universal Law of Gravitation - Question 23

Let x be the distance of the point of no net field from earth. The distance of this point from moon is (r – x), where r = 3.8 × 105 km.
The gravitational field due to earth = GMe/xand that due to moon = GMm/(r - x)2.
For the net field to be zero these are equal and opposite.


*Answer can only contain numeric values
Test: Universal Law of Gravitation - Question 24

A person brings a mass of 1 kg from infinity to a point A. Initially the mass was at rest but it moves at a speed of 2 m/s as it reaches A. The work done by the person on the mass is –3J. The potential at infinity is –10 J. Then find the potential at A.


Detailed Solution for Test: Universal Law of Gravitation - Question 24

Work done by external agent  
Went, = ΔU + ΔK
= UA – U + KA - K∞ 
= UA - 10 + 1/2 × mv2 - 0
- 3 = UA - 10 + 1/2  × 1  × 4
+ 5 J = U
So VA = 5 J/kg

*Answer can only contain numeric values
Test: Universal Law of Gravitation - Question 25

A cosmic body A moves towards star with velocity v0 (when far from the star) and aiming parameter L and arm of velocity vector v0 relative to the centre of the star as shown in figure. Find the minimum distance (take 108 m as unit) by which this body will get to the star. Mass of the star is M.


Detailed Solution for Test: Universal Law of Gravitation - Question 25

r =  minimum distance  
conservation of angular momentum about star mv0L = mrv

Solving,

Putting the values r = 3 × 108 m = 3 unit

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