Gravitation - Quiz 4

GRAVITATION QUIZ-4

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 mass of the earth is 81 times the mass of the Moon and the distance between the earth and the Moon is 60 times the radius of the earth. If R is the radius of the earth, then the distance between the Moon and the point on the line joining the Moon and the earth where the gravitational force becomes zero is

•  30R
•  15R
•   6R
•  5R

Solution

 

Q2.A spherical shell is cut into two pieces along a chord as shown in the figure. P is a point on the plane of the chord. The gravitational field at P due to the upper part is I₁ and due to the lower part is I₂. What is the relation between them?

•  I₁ > I₂
•  I₁ < I₂
•  I₁=I₂
•  No definite relation

Solution

Q3.Two bodies with masses M₁, and M₂ are initially at rest and a distance R apart. Then they move directly towards one another under the influence of their mutual gravitational attraction. What is the ratio of the distances travelled by M₁to the distance travelled by M₂?

•    M₁/M₂
•  M₂/M₁
•  1
•  1/2

Solution

Q4.A body of mass m rises to a height h=R/5 from the earth's surface where R is earth's radius. If g is acceleration due to gravity at the earth's surface, the increase in potential energy is

•  mgh
•  4/5 mgh
•  5/6 mgh
•  6/7 mgh

Solution

Q5.In problem 86, what is the gravitational potential energy of the mass m?

•  (-2/√3)  GMm/l(1-2√3)
•  (-2/√3)  GMm/l(1+2√3)
•  (-√3/2)  GMm/l (1-2√3)
•  (-√3/2)  GMm/l (1+2√3)

Solution

Q6.The earth moves around the Sun in an elliptical orbit as shown in figure. The ratio OA/OB=x. The ratio of the speed of the earth at B to that at A is nearly

•  √x
• x
•  x√x
•  x²

Solution

Q7.A space station is set up in space at a distance equal to the earth's radius from the surface of the earth. Suppose a satellite can be launched from the space station. Let v₁ and v₂ be the escape velocities of the satellite on the earth's surface and space station, respectively. Then

•  v₂=v₁
•  v₂<v₁
•  v₂ > v₁
•  (a), (b) and (c) are valid depending on the mass of satellite

Solution

Q8.A solid sphere of uniform density and mass M has radius 4 m. Its centre is at the origin of the coordinate system. Two spheres of radii 1 m are taken out so that their centres are at P(0,-2,0) and Q(0,2,0) respectively. This leaves two spherical cavities. What is the gravitational field at the origin of the coordinate axes?

•  31 GM/1024
•  Gm/1024
•  31 GM
•  Zero

Solution

Q9.The value of 'g' at a certain height h above the free surface of the earth is x/4 where x is the value of 'g' at the surface of the earth. The height h is

•  R
•  2R
•  3R
•  4R

Solution

Q10.The radius of a planet is R. A satellite revolves around it in a circle of radius r with angular velocity ω₀. The acceleration due to the gravity on planet's surface is

•  (r² ω₀)/R
•  (r³ ω₀³)/R²
•  (r³ ω₀²)/R
• (r³ ω₀²)/R²

Solution