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MCQ Practice Test & Solutions: Central Forces MCQ Level – 2 (10 Questions)

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Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 45 minutes
  • - Number of Questions: 10

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Central Forces MCQ Level – 2 - Question 1

The gravitational potential of two homogeneous spherical shells A and B of same surface density at their respective centres are in the ratio 3 : 4. If the two shells coalesce into single one such that surface density remains same, then the ratio of potential at an internal point of the new shell of shell A is equal to :

Detailed Solution: Question 1


 where σ is surface density


for New shell of mass M and radius R.


The correct answer is: 5 : 3

Central Forces MCQ Level – 2 - Question 2

A satellite is launched in the equatorial plane in such a way that it can transmit signals upto 60° latitude on the earth. The angular velocity of the satellite is :

Detailed Solution: Question 2

In  (where OR is orbital radius)
Here gravitational force will provide the required centripetal force.



The correct answer is: 

Central Forces MCQ Level – 2 - Question 3

A cavity of radius R/2 is made inside a solid sphere of radius R. The centre of the cavity is located at a distance R/2 from centre of the sphere. The gravitational force on a particle of mass m at a distance R/2 from the centre of the sphere on the line joining both the centres of sphere and cavity is (opposite to the centre of cavity).

[Here,  g = GM/R2, where  M is the mass of the sphere without cavity ]

Detailed Solution: Question 3

Gravitational field at mass 'm' due to full solid sphere 


Gravitational field at mass 'm' due to cavity (-ρ)

Net gravitational field 


Net force on m → 

The correct answer is: 3mg/8

Central Forces MCQ Level – 2 - Question 4

A tunnel is dug along the diameter of the earth (Radius R and mass ). There is a particle of mass m at the centre of the tunnel. The minimum velocity given to the particle so that it just reaches to the surface of the earth is :

Detailed Solution: Question 4

Let the minimum speed imparted to the particle of mass m so that it just reaches surface of earth is v. Applying conservation of energy


Solving we get 
The correct answer is: 

Central Forces MCQ Level – 2 - Question 5

Maximum height reached by a rocket fired with a speed equal to 50% of the escape velocity from earth’s surface is :

Detailed Solution: Question 5

Applying energy conservation  



The correct answer is: R/3

Central Forces MCQ Level – 2 - Question 6

The percentage change in the acceleration of the earth towards the sun from a total eclipse of the sun to the point where the moon is on a side of earth directly opposite to the sun is :

Detailed Solution: Question 6

During total eclipse-
Total attraction due to sun and moon.

When moon goes on the opposite side of earth.
Effective force of attraction,

Change in force, 
Change in acceleration of earth 
Average force on earth, 
Average acceleration of earth, 
%age change in acceleration 

The correct answer is: 

Central Forces MCQ Level – 2 - Question 7

A small area is removed from a uniform spherical shell of mass M and radius R. Then the gravitational field intensity near the hollow portion is :

Detailed Solution: Question 7

The Gravitational field at the centre of the hole due to the remaining mass is 

Central Forces MCQ Level – 2 - Question 8

A point P lies on the axis of a fixed ring of mass M and radius R, at a distance 2R from its centre O. A small particle starts from P and reaches O under gravitational attraction only. Its speed O will be

Detailed Solution: Question 8

Gravitational potential at ‘P


Gravitational potential at ‘O

work energy theorem 

The correct answer is: 

Central Forces MCQ Level – 2 - Question 9

Two particles of combined mass M, placed in space with certain separation, are released. Interaction between the particles is only of gravitational nature and there is no external force present. Acceleration of one particle with respect to the other when separation between them is R, has a magnitude :

Detailed Solution: Question 9


acceleration of M1 w.r.t. M2

The correct answer is: 

Central Forces MCQ Level – 2 - Question 10

Four similar particles of mass m are orbiting in a circle of radius r in the same angular direction because of their mutual gravitational attractive force. Velocity of a particle is given by :

Detailed Solution: Question 10

Centripetal force = net gravitational force


The correct answer is: 

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