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
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
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
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)
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?
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
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
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
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?
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)
Solution
