Gravitation

When one moves from a point 16 km below the earth's surface to a point 16 km above the earth's surface, the change in g is approximately %. The value of is . (Take radius of the earth = 6400 km.)

1. 0.12
2. 0.25
3. 0.50
4. 0.75

A body of mass m is taken from the surface of earth to a height equal to twice the radius of earth (Re). The increase in potential energy will be . (g is acceleration due to gravity at the surface of earth)

1. 12mgRe
2. 34mgRe
3. 14mgRe
4. 23mgRe

The height in terms of radius of the earth (R), at which the acceleration due to gravity becomes g9, where g is acceleration due to gravity on earth's surface, is .

1. 3R
2. 2 2R
3. 2R
4. 49R

A planet (P1) is moving around the star of mass 2M in the orbit of radius R. Another planet (P2) is moving around another star of mass 4M in an orbit of radius 2R. Ratio of time periods of revolution of P2 and P1 is .

1. 12
2. 2
3. 4
4. 14

If a body of mass 1 kg falls on the earth from infinity, it attains velocity (v) and kinetic energy (k) on reaching the surface of earth. The values of v and k respectively are . (Take radius of earth to be 6400 km and g=9.8 m/s2)

1. 11.2 km/s; 6.27 107 J
2. 11.2 km/s; 12.54 107 J
3. 8.8 km/s; 6.27 107 J
4. 8.8 km/s; 12.54 107 J

Three masses 200 kg, 300 kg and 400 kg are placed at the vertices of an equilateral triangle with sides 20 m. They are rearranged on the vertices of a bigger triangle of side 25 m and with the same centre. The work done in this process is J. (Gravitational constant G = 6.7 10-11 N m2/kg2)

1. 4.77 10-7
2. 1.74 10-7
3. 9.86 10-6
4. 2.85 10-7

The escape velocity from a spherical planet A is 10 km/s. The escape velocity from another planet B whose density and radius are 10\% of those of planet A, is m/s.

1. 1000
2. 200 5
3. 1000 2
4. 100 10

Net gravitational force at the center of a square is found to be F1 when four particles having mass M, 2M, 3M and 4M are placed at the four corners of the square as shown in figure and it is F2 when the positions of 3M and 4M are interchanged. The ratio F1F2 is 5. The value of is . [figure]

1. 2
2. 2 5
3. 1
4. 3

Given below are two statements : In the light of the above statements, choose the correct answer from the options given below :

1. Statement I is true but Statement II is false
2. Statement I is false but Statement II is true
3. Both Statement I and Statement II are true
4. Both Statement I and Statement II are false

Initially a satellite of 100 kg is in a circular orbit of radius 1.5RE. This satellite can be moved to a circular orbit of radius 3RE by supplying 106 J of energy. The value of is . (Take Radius of Earth RE = 6 106 m and g = 10 m/s2)

1. 500
2. 1000
3. 100
4. 150

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). In the light of the above statements, choose the most appropriate answer from the options given below:

1. (A) is not correct but (R) is correct
2. Both (A) and (R) are correct but (R) is not the correct explanation of (A)
3. Both (A) and (R) are correct and (R) is the correct explanation of (A)
4. (A) is correct but (R) is not correct

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R In the light of the above statements, choose the correct answer from the options given below

1. A is false but R is true
2. Both A and R are true and R is the correct explanation of A
3. A is true but R is false
4. Both A and R are true but R is NOT the correct explanation of A

An object is kept at rest at a distance of 3R above the earth's surface where R is earth's radius. The minimum speed with which it must be projected so that it does not return to earth is : (Assume M = mass of earth, G = Universal gravitational constant)

1. 3GMR
2. 2GMR
3. GM2R
4. GMR

Three identical spheres of mass m are placed at the vertices of an equilateral triangle of length a. When released, they interact only through gravitational force and collide after a time T = 4 seconds. If the sides of the triangle are increased to length 2a and also the masses of the spheres are made 2 m, then they will collide after seconds.

A satellite of mass 1000 kg is launched to revolve around the earth in an orbit at a height of 270 km from the earth's surface. Kinetic energy of the satellite in this orbit is 1010 J. (Mass of earth = 6 1024 kg, Radius of earth = 6.4 106 m, Gravitational constant = 6.67 10-11 N m2 kg-2)

Two planets, A and B are orbiting a common star in circular orbits of radii RA and RB, respectively, with RB=2RA. The planet B is 4 2 times more massive than planet A. The ratio ( LBLA ) of angular momentum (LB) of planet B to that of planet A (LA) is closest to integer .

Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 km/s, the escape velocity in km/s from the planet will be:

1. 8.4
2. 11.2
3. 5.6
4. 2.8

A satellite is launched into a circular orbit of radius 'R' around the earth. A second satellite is launched into an orbit of radius 1.03 R. The time period of revolution of the second satellite is larger than the first one approximately by

1. 3%
2. 2.5%
3. 4.5%
4. 9%

Acceleration due to gravity on the surface of earth is 'g'. If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of earth is g.

If a satellite orbiting the Earth is 9 times closer to the Earth than the Moon, what is the time period of rotation of the satellite? Given rotational time period of Moon = 27 days and gravitational attraction between the satellite and the moon is neglected.

1. 3 days
2. 27 days
3. 81 days
4. 1 day

A satellite of mass M2 is revolving around earth in a circular orbit at a height of R3 from earth surface. The angular momentum of the satellite is M GMRx. The value of x is , where M and R are the mass and radius of earth, respectively. ( G is the gravitational constant)

A small point of mass m is placed at a distance 2R from the centre ' O ' of a big uniform solid sphere of mass M and radius R . The gravitational force on ' m ' due to M is F1. A spherical part of radius R/3 is removed from the big sphere as shown in the figure and the gravitational force on m due to remaining part of M is found to be F2. The value of ratio F1:F2 is [figure]

1. 11 : 10
2. 12 : 11
3. 16 : 9
4. 12 : 9