Gravitation

The amount of work done to raise a mass 'm' from the surface of the Earth to a height equal to the radius of the Earth 'R' will be :

1. mg R2
2. mgR
3. mg R4
4. 2mgR

Two planets P1 and P2 with equal mass have radii R1 and R2, respectively, where R2 = R12. The escape speeds of P1 and P2 are v1 and v2, respectively. Then v2v1 is:

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

In a solar system, the time-period of revolution of a planet tracing a circular orbit of radius R is proportional to:

1. R3
2. R1/2
3. R3/2
4. R2

The radius of Martian orbit around the Sun is about 4 times the radius of the orbit of Mercury. The Martian year is 687 Earth days. Then which of the following is the length of 1 year on Mercury?

1. 172 earth days
2. 124 earth days
3. 88 earth days
4. 225 earth days

A body weighs 48 N on the surface of the earth. The gravitational force experienced by the body due to the earth at a height equal to one-third the radius of the earth from its surface is:

1. 32 N
2. 36 N
3. 16 N
4. 27 N

The mass of a planet is 110th that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is:

1. 19.6 m s-2
2. 9.8 m s-2
3. 4.9 m s-2
4. 3.92 m s-2

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

1. 5GmM6R
2. 2GmM3R
3. GmM2R
4. GmM3R

The escape velocity for earth is v. A planet having 9 times mass that of earth and radius, 16 times that of earth, has the escape velocity of:

1. v3
2. 2v3
3. 3v4
4. 9v4

An object of mass 100 kg falls from point A to B as shown in figure. The change in its weight, corrected to the nearest integer is (RE is the radius of the earth) [figure]

1. 49 N
2. 89 N
3. 5 N
4. 10 N

Two bodies of mass m and 9m are placed at a distance R. The gravitational potential on the line joining the bodies where the gravitational field equals zero, will be (G = gravitational constant) :

1. - 12GmR
2. - 16GmR
3. - 20GmR
4. - 8GmR

A satellite is orbiting just above the surface of the earth with period T. If d is the density of the earth and G is the universal constant of gravitation, the quantity 3 Gd represents :

1. T2
2. T3
3. T
4. T

A body of mass 60 g experiences a gravitational force of 3.0 N, when placed at a particular point. The magnitude of the gravitational field intensity at that point is

1. 0.05 N/kg
2. 50 N/kg
3. 20 N/kg
4. 180 N/kg

A gravitational field is present in a region and a mass is shifted from A to B through different paths as shown. If W1, W2 and W3 represent the work done by the gravitational force along the respective paths, then : [figure]

1. W1 < W2 < W3
2. W1 = W2 = W3
3. W1 > W2 > W3
4. W1 > W3 > W2

In a gravitational field, the gravitational potential is given by, V = - Kx (J/Kg). The gravitational field intensity at point (2, 0, 3) m is

1. + K4
2. + K2
3. - K2
4. - K4

The escape velocity from the Earth's surface is v. The escape velocity from the surface of another planet having a radius, four times that of Earth and same mass density is :

1. 4v
2. v
3. 2v
4. 3v

A particle of mass 'm' is projected with a velocity v = kVe (k < 1) from the surface of the earth. (Ve = escape velocity) The maximum height above the surface reached by the particle is :

1. Rk21-k2
2. R ( k1-k2 )2
3. R ( k1+k2 )2
4. R2k1+k

A body weighs 72 N on the surface of the earth. What is the gravitational force on it, at a height equal to half the radius of the earth?

1. 32 N
2. 30 N
3. 24 N
4. 48 N

The work done to raise a mass m from the surface of the earth to a height h, which is equal to the radius of the earth, is :

1. mgR
2. 2mgR
3. 12mgR
4. 32mgR

A body weighs 200 N on the surface of earth. How much will it weigh half way down to the centre of the earth?

1. 200 N
2. 250 N
3. 100 N
4. 150 N

The kinetic energies of a planet in an elliptical orbit about the Sun, at positions A, B and C are KA, KB and KC, respectively. AC is the major axis and SB is perpendicular to AC at the position of the Sun S as shown in the figure. Then [figure]

1. KA < KB < KC
2. KA > KB > KC
3. KB < KA < KC
4. KB > KA > KC

If the mass of the Sun were ten times smaller and the universal gravitational constant were ten times larger in magnitude, which of the following is not correct?

1. Raindrops will fall faster.
2. Walking on the ground would become more difficult.
3. Time period of a simple pendulum on the Earth would decrease.
4. g on the Earth will not change.

The acceleration due to gravity at a height 1 km above the earth is the same as at a depth d below the surface of earth. Then

1. d = 1 km
2. d = 32 km
3. d = 2 km
4. d = 12 km

Two astronauts are floating in gravitational free space after having lost contact with their spaceship. The two will

1. move towards each other.
2. move away from each other.
3. will become stationary.
4. keep floating at the same distance between them.

At what height from the surface of earth the gravitation potential and the value of g are -5.4 107 J kg-1 and 6.0 m s-2 respectively? Take the radius of earth as 6400 km.

1. 1400 km
2. 2000 km
3. 2600 km
4. 1600 km

The ratio of escape velocity at earth (ve) to the escape velocity at a planet (vp) whose radius and mean density are twice as that of earth is

1. 1 : 4
2. 1 : 2
3. 1 : 2
4. 1 : 2 2

Starting from the centre of the earth having radius R, the variation of g (acceleration due to gravity) is shown by

1. [figure]
2. [figure]
3. [figure]
4. [figure]

A satellite of mass m is orbiting the earth (of radius R) at a height h from its surface. The total energy of the satellite in terms of g0, the value of acceleration due to gravity at the earth's surface, is

1. mg0R22(R+h)
2. - mg0R22(R+h)
3. 2mg0R2R+h
4. - 2mg0R2R+h

A remote-sensing satellite of earth revolves in a circular orbit at a height of 0.25 106 m above the surface of earth. If earth's radius is 6.38 106 m and g = 9.8 m s-2, then the orbital speed of the satellite is

1. 9.13 km s-1
2. 6.67 km s-1
3. 7.76 km s-1
4. 8.56 km s-1

A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then,

1. the linear momentum of S remains constant in magnitude.
2. the acceleration of S is always directed towards the centre of the earth.
3. the angular momentum of S about the centre of the earth changes in direction, but its magnitude remains constant.
4. the total mechanical energy of S varies periodically with time.

Kepler's third law states that square of period of revolution (T) of a planet around the sun, is proportional to third power of average distance r between sun and planet i.e. T2 = Kr3 here K is constant. If the masses of sun and planet are M and m respectively then as per Newton's law of gravitation force of attraction between them is F = GMmr2, here G is gravitational constant. The relation between G and K is described as

1. K = G
2. K = 1G
3. GK = 4 2
4. GMK = 4 2