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GRAVITATION QUIZ-3

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. A tunnel is dug along the diameter of the earth (radius R and mass M). 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

  •  √(GM/R)
  •  √(GM/2R)
  •   √(2GM/R)
  •  It will reach with the help of a negligible velocity
Solution




 

Q2.Three uniform spheres, each having mass m and radius r, are kept in such a way that each touches the other two. The magnitude of the gravitational force on any sphere due to the other two is
  •  (Gm2)/r2
  •  (Gm2)/(4r2 )
  •  √2 (Gm2)/(4r2)
  •  √3 (Gm2)/(4r2 )
Solution




Q3.Two equal masses each m are hung from a balance whose scale pans differ in vertical height by 'h'. The error in weighing in terms of density of the earth ρ is

  •    πGρmh
  •  1/3 πGρmh
  •  8/3 πGρmh
  •  4/3 πGρmh
Solution



Q4.What should be the angular velocity of rotation of the earth about its own axis so that the weight of a body at the equator reduces to 3/5 or its present value? (Take R as the radius of the earth)
  •  √(g/3R)
  •  √(2g/3R)
  •  √(2g/5R)
  •  √(2g/7R)
Solution




Q5.Consider two solid uniform spherical objects of the same density ρ. One has radius R and te other has radius 2R. They are in outer space where the gravitational fields from other objects are negligible. If they are arranged with their surface touching, what is the contact force between the objects due to their traditional attraction?
  •  2 R4
  •  128/81 Gπ2 R4 ρ2
  •  128/81 Gπ2
  •  127/87 π2R2G
Solution




Q6.A satellite of mass m is in an elliptical orbit around the earth. The speed of the satellite at its nearest position is (6GMe )/(5r) where r is the perigee (nearest point) distance from the centre of the earth. It is desired to transfer the satellite to the circular orbit of radius equal to its apogee (farthest point) distance from the centre of the earth. The change in orbital speed required for this purpose is
  •  0.35(GMe/r)1/2
  • 0.085(GMe/r)1/2
  •  (2GMe/r)1/2
  •  Zero
Solution




Q7.Two satellites of the same mass are launched in the same orbit around the earth so as to rotate opposite to each other. If they collide inelastically and stick together as wreckage, the total energy of the system just after collision is
  •  -2GMm/r
  •  -GMm/r
  •  GMm/2r
  •  GMm/4r
Solution




Q8.Te radius of the earth is about 6400 km and that of Mars is about 3200 km. The mass of the earth is about 10 times the mass of Mars. An object weights 200 N on the surface of the earth. Its weight on the surface of mars would be
  •  6N
  •  20N
  •  40N
  •  80N
Solution




Q9.Two astronauts have deserted their spaceship in a region of space far from the gravitational attraction of any other body. Each has a mass of 100 kg and they are 100 m apart. They are initially at rest relative to one another. How long will it be before the gravitational attraction brings them 1 cm closer together?
  •  2.52 days
  •  1.41 days
  •  0.70 days
  •  1.41 s
Solution





Q10.The distances from the centre of the earth, where the weight of a body is zero and one-fourth that of the weight of the body on the surface of the earth are (assume R is the radius of the earth)
  •  0 , R/4
  •  0 , 3R/4
  •  R/4 , 0
  • 3R/4 , 0
Solution




 


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Gravitation - Quiz 3
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