Gravitation - Quiz 5

GRAVITATION QUIZ-5

Dear Readers,

JEE Advanced Physics Syllabus can be referred by the IIT aspirants to get a detailed list of all topics that are important in cracking the entrance examination. JEE Advanced syllabus for Physics has been designed in such a way that it offers very practical and application-based learning to further make it easier for students to understand every concept or topic by correlating it with day-to-day experiences. In comparison to the other two subjects, the syllabus of JEE Advanced for physics is developed in such a way so as to test the deep understanding and application of concepts.

Gravitation is an easy to understand and a highly scoring topic. It might have a 1% weightage in the entire JEE Physics portion but do not neglect. You can practice these questions on regular basis to know what are the important points to remember at the moment when gravitation question comes.

Q1.The gravitational potential due to earth at infinite distance from it is zero. Let the gravitational potential at a point P be -5 J kg^-1. Suppose, we arbitarily assume the gravitational potential at infinity to be +10 J kg^-1, then the gravitational potential at P will be

•  -5 J kg^-1
•  +5 J kg^-1
•   -15 J kg^-1
•  +15 J kg^-1

Solution

Q2.Two satellite A and B of masses m₁ and m₂ (m₁=2 m₂) are moving in circular orbits of radii r₁ and r₂ (r₁=4r₂), respectively, around the earth. If their periods are T_A and T_B, then the ratio T_A/T_B is

•  4
•  16
•  2
•  8

Solution

Q3.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

•    [Gm/r ((1+2√2)/4)]^(1/2)
•  √(Gm/r)
•  √(Gm/r(1+2√2))
•  [1/2 Gm/r ((1+2√2)/2)]^(1/2)

Solution

Q4.A spherically symmetric gravitational system of particles has a mass density 

 ρ={(ρ₀ for r≤R
      {0 for r>R 

 where ρ₀ is a constant. A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed v as a function of distance r(0 <r < ∞) from the centre of the system is represented by

•  
  
  
  
•  
  
  
  
  
  
  
  
•  
  
  
  
•  
  
  
  

Solution

Q5.If g is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass m raised from the surface of the earth to a height equal to the radius R of the earth is

•  1/2 mgR
•  2 mgR
•  mgR
•  1/4 mgR

Solution

Q6.A satellite of mass m is orbitiing around the earth at a height h above the surface of the earth. Mass of the earth is M and its radius is R. The angular momentum of the satellite is independent of

•  m
• M
•  h
•  None of these

Solution

Q7.A ring having non-uniform distribution of mass M and radius R is being considered. A point mass m₀ is taken slowly towards the ring. In doing so, work done by the external force against the gravitational force exerted by ring is

•  (GMm₀)/(√2 R)
•  (GMm₀)/R [1/√2 - 1/√5]
•  (GMm₀)/R [1/√5 - 1/√2]
•  It is not possible to find the required work as the nature of distribution of mass is not known

Solution

Q8.Four particles, each of mass M, move along a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is

•  GM/R
•  √(2√2 GM/R)
•  √(GM/R(2√2+1))
•  √(GM/R ((2√2+1)/4) )

Solution

Q9.Two concentric shells of masses M₁ and M₂ are having radii r₁ and r₂. Which of the following is the correct expression for the gravitational filed on a mass m?

                                                        

•  F=(G(M₁+M₂))/r² , for r <r₁
•  F=(G(M₁+M₂))/r² , for r <r₂
•  F=(GM₂)/r² , for r₁< r <r₂
•  F=(GM₁)/r² , for r₁< r <r₂

Solution

Q10.Gravitational acceleration on the surface of a planet is √6/11 g, where g is the gravitational acceleration on the surface of earth. The average mass density of the planet is 2/( 3) times that of the earth. If the escape speed on the surface of the earth is taken on be 11 kms^-1, the escape speed on the surface of the planet in kms^-1 will be

•  5
•  7
•  3
• 11

Solution