Types Of Questions

## Gravitation

- Wondering what kind of questions that can be asked in next exam? Here you go
1
JEE Mains
Single Choice Type
Two metal spheres of the same material and radius are in contact with each other. The gravitational force of attraction between the spheres is given by:
A
B
C
D
From a sphere of mass and radius , a smaller sphere of radius is carved out such that the cavity made in the original sphere is between its centre and the periphery. (See figure). For the configuration in the figure where the distance between the centre of the original sphere and the removed sphere is , the gravitational force between the two spheres is :
A
B
C
D
A particle is moving with speed along positive x-axis. Calculate the speed of the particle at time (assume that the particle is at origin at )
A
B
C
D
The position of a particle as a function of time t, is given by where a, b and c are constants. When the particle attains zero acceleration, then its velocity will be?
A
B
C
D
A satellite is seen after each over the equator at a place on the earth when its sense of rotation is opposite to the earth. The time interval after which it can be seen at the same place when the sense of rotation of the earth and the satellite is the same will be
A
B
C
D
Two satellites are revolving round the earth at different heights. The ratio of their orbital speeds is . If one of them is at a height of , the height of the other satellite is Radius of earth km
A
19600 km
B
24600 km
C
29600 km
D
14600 km
An object is projected vertically upwards from the surface of the earth with a velocity times the escape velocity from earth's surface. What will be its final velocity after escape from the earth's gravitational pull?
A
B
C
D
2
Blank Type
A particle of mass m is placed at a distance of from the centre of a huge uniform sphere of mass and radius . A spherical cavity of diameter is made in the sphere as shown in the figure. If the gravitational interaction potential energy of the system of mass and the remaining sphere after making the cavity is  Find the value of
An artificial satellite is launched into a circular orbit around the Earth with velocity v relative to the reference frame moving translationally and fixed to the Earth's rotation axis. The distance from the satellite to the Earth's surface. Find .  The radius of the Earth  and the free-fall acceleration on its surface are supposed to be known.
Gravitational acceleration on the surface of a planet is , where is the gravitational acceleration on the surface of the earth. The average mass density of the planet is times that of the earth. If the escape speed on the surface of the earth is taken to be 11 kms , the escape speed on the surface of the planet in kms will be
3
Single Correct
A solid sphere of uniform density and radius applies a gravitational force of attraction equal to on a particle placed at a distance 3R from the centre of the sphere. A spherical cavity of radius  is now made in the sphere, as shown in the figure. The sphere with cavity now applies a gravitational force  on the same particle. The ratio  is
A
B
C
D
A rocket is launched normal to the surface of the Earth, away from the Sun, along the line, joining the Sun and the Earth. The Sun is times heavier than the Earth and is at a distance times larger than the radius of the Earth. The escape velocity from Earth's gravitational field is . The minimum initial velocity required for the rocket to be able to leave the Sun-Earth system is closest to (Ignore the rotation and revolution of the Earth and the presence of any other planet)
A
B
C
D
Two bodies, each of mass are kept fixed at a separation . A particle of mass m is projected from the midpoint of the line joining their centres, perpendicular to the line. The gravitational constant is The correct statement(s) is (are)
A
The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is
B
The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is
C
The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is
D
The energy of the mass m remains constant.
Three particles, each of mass are situated at the vertices of an equilateral triangle of side . The only forces acting on the particles are their mutual gravitational forces. It is desired that each particle should move in a circle while maintaining the original mutual separation . Then their time period of revolution is :
A
B
C
D
A satellite is seen after each over the equator at a place on the earth when its sense of rotation is opposite to the earth. The time interval after which it can be seen at the same place when the sense of rotation of the earth and the satellite is the same will be
A
B
C
D
4
Multiple Correct
Two planets A, B have their radii in the ratio and densities in the ratio respectively. Choose the correct statement(s)
This question has multiple correct options
A
The ratio of the acceleration due to gravity on them is
B
For the same volume of planets, the mass of planet A is greater than that of planet B.
C
A body weighs times more on planet B than on planet A.
D
Planet B has a greater volume than planet A.
An object is weighed at the North pole by a beam balance and a spring balance, giving readings of  and respectively. It is again weighed in the same manner at the equator, giving reading of  and respectively. Assume that the acceleration due to gravity is the same everywhere and that the balances are quite sensitive.
This question has multiple correct options
A
B
C
D
Inside a uniform spherical shell
This question has multiple correct options
A
The gravitational potential is zero
B
The gravitational field is zero
C
The gravitational potential is same everywhere
D
The gravitational field is same everywhere.
5
Numerical Type I
A bullet is fired vertically upwards with velocity from the surface of a spherical planet. When it reaches its maximum heights, its acceleration due to the planet's gravity is th of its value at the surface of the planet. If the escape velocity from the planet is , then the value of N is (ignore energy loss due to atmosphere)
lmagine a vertical mine shaft of depth x metres located near the equator (of earth). A plumb line is hanging in the shaft and a stone is dropped from rest next to it. The stone will not fall parallel to the plumb line, but will deviate in easterly direction by an amount of y metres.
Given is angular speed of earth and is acceleration due to gravity)
If y find n.
6
Numerical Type II
A large spherical mass M is fixed at one position and two identical point masses m are kept on a line passing through the centre of M. The point masses are connected by a rigid massless rod of length and this assembly is free to move along the line connecting them. All three masses interact only through their mutual gravitational interaction. When the point mass nearer to M is at a distance from M, the tension in the rod is zero for . The value of k is
A particle of mass m is placed at a distance of from the centre of a huge uniform sphere of mass and radius . A spherical cavity of diameter is made in the sphere as shown in the figure. If the gravitational interaction potential energy of the system of mass and the remaining sphere after making the cavity is  Find the value of
7
Matrix Match Type
A planet of mass M, has two natural satellites with masses and . The radii of their circular orbits are and respectively. Ignore the gravitational force between the satellites. Define and to be respectively, the orbital speed, angular momentum, kinetic energy and time period of revolution of satellite ; and and to be the corresponding quantities of satellite . Given and , match the ratios in List - I to the numbers in List-II.

 List - I List - II P. 1. Q. 2. R. 3. S. 4.

A
B
C
D
Match the following.
List 1The escape velocity is independent ofAtmosphere on a planet depends onAcceleration due to gravity is independent ofPotential energy of planet mass system is independent of
List 2Direction of projectionMass of the planetMass of the bodyEscape velocity for the planetTemperature of the planet surface
8
Assertion Reason Type
Assertion
The value of escape velocity from the surface of earth at and is
Reason
The value of escape velocity is independent of angle of projection.
A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C
Assertion is incorrect but Reason is correct
D
Both Assertion and Reason are incorrect
Assertion
Escape velocity is independent of the angle of projection.
Reason
Escape velocity from the surface of earth is where R is radius of earth.
A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C
Assertion is correct but Reason is incorrect
D
Both Assertion and Reason are incorrect
Assertion
Two satellites are following one another in the same circular orbit. If one satellite tries to catch another (leading one) satellite, then it can be done by increasing its speed without changing the orbit.
Reason
The energy of the earth-satellite system in a circular orbit is given by , where r is the radius of the circular orbit.
A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C
Assertion is incorrect but Reason is correct
D
Both Assertion and Reason are incorrect
9
Passage Type
The value of will be
A
B
C
D
What is the gravitational field at Q?
A
B
C
D
Inside a uniform sphere of density there is a spherical cavity whose centre is at a distance  from the centre of the sphere. Find the strength  of the gravitational field inside the cavity.