Gravitation - Quiz 8

GRAVITATION QUIZ-8

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.In the solar system, the Sun is in the focus of the system for Sun-earth binding system. Then the binding energy for the system will be [given that radius of the earth's orbit round the Sun is 1.5×10¹¹m and mass of the earth =6×10²⁴ kg]

•  2.7×10³³ J
•  5.4×10³³ J
•  2.7×10³⁰ J
•  5.4×10³⁰ J

Solution

 

Q2.Two particles of equal mass go around a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is

•  v=1/2R√Gm
•  v=√(Gm/2R)
•  v=√Gm/√2R
•  v=√(4Gm/R)

Solution

Q3.What is the mass of the planet that has a satellite whose time period is T and orbital radius is r?

•  (4π² r³)/(GT² )
•  (4π² r³)/(GT² )
•  (4π² r³)/(GT³ )
•  (4π² T)/(GT² )

Solution

Q4.The escape velocity corresponding to a planet of mass M and radius R is 50 km s^-1. If the planet's mass and radius were 4M and R, respectively, then the corresponding escape velocity would be

•  100 km s^-1
•  50 km s^-1
•  200 km s^-1
•  25 km s^-1

Solution

Q5.A point P is on the axis of a fixed ring of mass M and radius R, at a distance 2R from the centre O. A small particle starts from P and reaches O under the gravitational attraction only. Its speed at O will be

•  Zero
•  √(2GM/R)
•  √(2GM(√5-1)/R)
•  √(2GM(1 - 1/√5)/R)

Solution

Q6.Masses of 1 kg each are placed 1 m, 2 m, 4 m, 8 m,... from a point P. The gravitational field intensity at P due to these masses is

•  G
•  G
•  4G
•  4G/3

Solution

Q7.A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth

•  The acceleration of S is always directed towards the centre of the earth
•  The angular momentum of S about the centre of the earth changes in direction, but its magnitude remains constant
•  The total mechanical energy of S varies periodically with time
•  The linear momentum of S remains constant in magnitude

Solution

Q8.A uniform ring of mass m and radius r is placed directly above a uniform sphere of mass M and of equal radius. The centre of the ring is directly above the centre of the sphere at a distance r√3 as shown in the figure. The gravitational force exerted by the sphere on the ring will be

•  GMm/(8r² )
•  GMm/(4r² )
•  √3 GMm/(8r² )
•  GMm/(8r³ √3)

Solution

Q9.The minimum energy required to launch a m kg satellite from the earth's surface in a circular orbit at an altitude 2R, where R is the radius of earth is

•  5mgR/3
•  4mgR/3
•  5mgR/6
•  5mgR/4

Solution

Q10.The masses and radii of the earth and the Moon are M₁,R₁ and M₂,R₂, respectively. Their centres are at distance d apart. The minimum speed with which a particle of mass m should be projected from a point midway the two centres so as to escape to infinity is

•  √(2G(M₁+M₂)/d)
•  √(4G(M₁+M₂)/d)
•  √(4GM₁ M₂)/d)
• √(G(M₁+M₂)/d)

Solution