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Test: 35 Year JEE Previous Year Questions: Gravitation


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24 Questions MCQ Test Physics For JEE | Test: 35 Year JEE Previous Year Questions: Gravitation

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Test: 35 Year JEE Previous Year Questions: Gravitation - Question 1

STATEMENT - 1 : An astronaut in an orbiting space station above the earth experiences weightlessness. because
STATEMENT - 2 :  An object moving the earth under the influence of Earth’s gravitational force is in a state of “freefall”.

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Gravitation - Question 1

The normal force exerted by the astronaut on orbiting space station is zero (until the astronaut exerts some muscular force). Therefore the apparent weight of astronaut in an orbiting space station is zero. Astronaut is called in a state of weightlessness. This is because astronaut as well as space -ship are freely falling bodies.
Statement - 1 is true, statement - 2 is true and statement - 2 is the correct explanation of statement - 1.

Test: 35 Year JEE Previous Year Questions: Gravitation - Question 2

The kinetic energy needed to project a body of mass m from the earth surface (radius R) to infinity is

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Gravitation - Question 2

 where ve = escape velocity 

Test: 35 Year JEE Previous Year Questions: Gravitation - Question 3

If suddenly the gravitational force of attraction between Earth and a satellite revolving around it becomes zero, then the satellite will

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Gravitation - Question 3

Due to inertia of motion it will move tangentially to the original orbit in the same velocity.

Test: 35 Year JEE Previous Year Questions: Gravitation - Question 4

Energy required to move a body of mass m from an orbit of radius 2R to 3R is

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Gravitation - Question 4

Energy required = (Potential energy of the Earth -mass system when mass is at distance 3R) – (Potential energy of the Earth -mass system when mass is at distance 2R)

Test: 35 Year JEE Previous Year Questions: Gravitation - Question 5

The escape velocity of a body depends upon mass as

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Gravitation - Question 5

Escape velocity, 

Where M, R are the mass and radius of the planet respectively. In this expression the mass of the body (m) is not present showing that the escape velocity is independent of the mass.

Test: 35 Year JEE Previous Year Questions: Gravitation - Question 6

The time period of a satellite of earth is 5 hours. If the separation between the earth and the satellite is increased to 4 times the previous value, the new time period will become

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Gravitation - Question 6

According to Kepler ’s law of planetary motion T2 ∝ R3

Test: 35 Year JEE Previous Year Questions: Gravitation - Question 7

Two spherical bodies of mass M and 5M & radii R & 2R respectively are released in free space with initial separation between their centres equal to 12 R. If they attract each other due to gravitational force only, then  the distance covered by the smaller body  just before collision is

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Gravitation - Question 7

The gravitational force acting on both the masses is the same. We know that

Force = mass × acceleration.

For same force,   acceleration  

                .....(i)

Let t be the time taken for the two masses to collide and x5M, xM be the distance travelled by the mass 5M and M respectively.

For mass 5M
For mass M

Dividing (ii) by (iii)

From the figure it is clear that

x5M+ xM = 9R                ....(v)
Where O is the point where the two spheres collide.
From (iv) and (v)

∴ 6 xM= 45R 

Test: 35 Year JEE Previous Year Questions: Gravitation - Question 8

The escape velocity for a body projected vertically upwards from the surface of earth is 11 km/s. If the body is projected at an angle of 45°with the vertical, the escape velocity will be

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Gravitation - Question 8

The escape velocity is independent of the angle at which the body is projected.

Test: 35 Year JEE Previous Year Questions: Gravitation - Question 9

A satellite of mass m revolves around the earth of radius R at a height x from its surface. If g is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Gravitation - Question 9

Gravitational force provides the necessary centripetal force.

Test: 35 Year JEE Previous Year Questions: Gravitation - Question 10

The time period of an earth satellite in circular orbit is independent of

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Gravitation - Question 10

x = height  of satellite from earth surface
m = mass of satellite

which is independent of mass of satellite

Test: 35 Year JEE Previous Year Questions: Gravitation - Question 11

If ‘g’ is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of an object of mass ‘m’ raised from the surface of the earth to a height equal to the radius ‘R' of the earth is

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Gravitation - Question 11

Test: 35 Year JEE Previous Year Questions: Gravitation - Question 12

Suppose the gravitational force varies inversely as the nth power of distance. Then the time period of a planet in circular orbit of radius ‘R’ around the sun will be proportional to

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Gravitation - Question 12

Test: 35 Year JEE Previous Year Questions: Gravitation - Question 13

The change in the value of ‘g’ at a height ‘h’ above the surface of the earth is the same as at a depth ‘d’ below the surface of earth. When both ‘d’ and ‘h’ are much smaller than the radius of earth, then which one of the following is correct ?

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Gravitation - Question 13

Variation of g with altitude is,  

variation of g with depth is 

Equating gh and gd , we get d = 2h

Test: 35 Year JEE Previous Year Questions: Gravitation - Question 14

A particle of mass 10 g is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm. Find the work to be done against the gravitational force between them to take the particle far away from the sphere  (you may take G = 6.67× 10-11 Nm2 / kg2)

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Gravitation - Question 14

Test: 35 Year JEE Previous Year Questions: Gravitation - Question 15

Average density of the earth

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Gravitation - Question 15

Test: 35 Year JEE Previous Year Questions: Gravitation - Question 16

A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is 11 km s–1, the escape velocity from the surface of the planet would be

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Gravitation - Question 16

Test: 35 Year JEE Previous Year Questions: Gravitation - Question 17

This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements. 

Statement-1 : For a mass M kept at the centre of a cube of side ‘a’, the flux of gravitational field passing through its sides 4 π GM.

Statement-2: If the direction of a field due to a point source is radial and its dependence on the distance ‘r’ from the source is given
as   its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface.

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Gravitation - Question 17

Gravitational  flux through a closed surface is given by

where, M = mass enclosed in the closed surface

This relationship is valid when 

Test: 35 Year JEE Previous Year Questions: Gravitation - Question 18

The height at which the acceleration due to gravity becomes 8/9 (where g = the acceleration due to gravity on the surface of the earth) in terms of R, the radius of the earth, is :

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Gravitation - Question 18

Test: 35 Year JEE Previous Year Questions: Gravitation - Question 19

Two bodies of masses m and 4 m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is:

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Gravitation - Question 19

Let the gravitational field at P, distant x from mass m, be zero.


Gravitational potential at  

Test: 35 Year JEE Previous Year Questions: Gravitation - Question 20

The mass of a spaceship is 1000 kg. It is to be launched from the earth's surface out into free space. The value of g and R (radius of earth) are 10 m/s2 and 6400 km respectively. The required energy for this work will be :

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Gravitation - Question 20

The required energy for this work is given by

Test: 35 Year JEE Previous Year Questions: Gravitation - Question 21

What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of  2R? 

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Gravitation - Question 21

Applying energy conservation

Test: 35 Year JEE Previous Year Questions: Gravitation - Question 22

Four particles, each of mass M and equidistant from each other, move along a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle is:

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Gravitation - Question 22


Test: 35 Year JEE Previous Year Questions: Gravitation - Question 23

From a solid sphere of mass M and radius R, a spherical portion of radius R/2 is removed, as shown in the figure.
Taking gravitational potential V = 0 at r = ∞, the potential at the centre of the cavity thus formed is :     

(G = gravitational constant)

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Gravitation - Question 23

Due to complete solid sphere, potential at point P


Due to cavity part potential at point P

So potential at the centre of cavity

Test: 35 Year JEE Previous Year Questions: Gravitation - Question 24

A satellite is revolving in a circular orbit at a height 'h' from the earth's surface (radius of earth R; h < < R). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth's gravitational field, is close to : (Neglect the effect of atmosphere.)

Detailed Solution for Test: 35 Year JEE Previous Year Questions: Gravitation - Question 24

For h << R, the orbital velocity is 

Escape velocity 

∴ The minimum increase in its orbital velocity

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