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

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%

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 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

An astronaut takes a ball of mass m from earth to space. He throws the ball into a circular orbit about earth at an altitude of 318.5 km. From earth's surface to the orbit, the change in total mechanical energy of the ball is x GMe m21Re. The value of x is (take Re = 6370 km) :

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

A satellite of 103 kg mass is revolving in circular orbit of radius 2R. If 104R6 J energy is supplied to the satellite, it would revolve in a new circular orbit of radius (use g = 10 m/s2, R = radius of earth)

1. 4R
2. 6R
3. 2.5R
4. 3R

Two planets A and B having masses m1 and m2 move around the sun in circular orbits of r1 and r2 radii respectively. If angular momentum of A is L and that of B is 3L, the ratio of time period ( TATB ) is:

1. ( r2r1 ) 32
2. 27 ( m1m2 )3
3. ( r1r2 )3
4. 127 ( m2m1 )3

Two satellites A and B go round a planet in circular orbits having radii 4R and R respectively. If the speed of A is 3v, the speed of B will be :

1. 6v
2. 43v
3. 3v
4. 12v

To project a body of mass m from earth's surface to infinity, the required kinetic energy is (assume, the radius of earth is RE, g = acceleration due to gravity on the surface of earth):

1. 12mgRE
2. 4mgRE
3. mgRE
4. 2mgRE

Assuming the earth to be a sphere of uniform mass density, a body weighed 300 N on the surface of earth. How much it would weigh at R/4 depth under surface of earth ?

1. 75 N
2. 375 N
3. 300 N
4. 225 N

A simple pendulum doing small oscillations at a place R height above earth surface has time period of T1 = 4 s. T2 would be its time period if it is brought to a point which is at a height 2R from earth surface. Choose the correct relation [R = radius of earth] :

1. 3T1 = 2T2
2. T1 = T2
3. 2T1 = 3T2
4. 2T1 = T2

A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius of orbit of the satellite is : (Given: Radius of geo-stationary orbit for earth is 4.2 104 km)

1. 1.68 105 km
2. 1.4 104 km
3. 8.4 104 km
4. 1.05 104 km

A metal wire of uniform mass density having length L and mass M is bent to form a semicircular arc and a particle of mass m is placed at the centre of the arc. The gravitational force on the particle by the wire is :

1. GmM 2L2
2. GMm 2L2
3. 0
4. 2GmM L2

A 90 kg body placed at 2R distance from surface of earth experiences gravitational pull of : (R = Radius of earth, g = 10 m s-2)

1. 300 N
2. 225 N
3. 100 N
4. 120 N

Correct formula for height of a satellite from earth's surface is :

1. ( T2R2g4 2 )1/3 - R
2. ( T2R2g4 )1/2 - R
3. ( T2R2g4 2 )-1/3 + R
4. ( T2R24 2g )1/3 - R

If R is the radius of the earth and the acceleration due to gravity on the surface of earth is g= 2 m/s2, then the length of the second's pendulum at a height h=2R from the surface of earth will be :

1. 19 m
2. 89 m
3. 29 m
4. 49 m

A light planet is revolving around a massive star in a circular orbit of radius R with a period of revolution T. If the force of attraction between planet and star is proportional to R-3/2 then choose the correct option :

1. T2 R7/2
2. T2 R3
3. T2 R5/2
4. T2 R3/2