Gravitation

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

Four identical particles of mass m are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is ( 2 2+132 ) Gm2L2, the length of the sides of the square is

1. 4L
2. 3L
3. 2L
4. L2

The mass of the moon is 1144 times the mass of a planet and its diameter is 116 times the diameter of a planet. If the escape velocity on the planet is v, the escape velocity on the moon will be :

1. v4
2. v6
3. v12
4. v3

The gravitational potential at a point above the surface of earth is -5.12 107 J/kg and the acceleration due to gravity at that point is 6.4 m/s2. Assume that the mean radius of earth to be 6400 km. The height of this point above the earth's surface is :

1. 1600 km
2. 1200 km
3. 540 km
4. 1000 km

Escape velocity of a body from earth is 11.2 km/s. If the radius of a planet be one-third the radius of earth and mass be one-sixth that of earth, the escape velocity from the planet is :

1. 7.9 km/s
2. 8.4 km/s
3. 4.2 km/s
4. 11.2 km/s

At what distance above and below the surface of the earth a body will have same weight. (take radius of earth as R.)

1. 3R-R2
2. R2
3. 5R-R2
4. 5R-R