If the gravitational force between two object were proportional to ^{1}/R (and not as^{ 1}/R^{2}), where R is separation between them, then a particle in circular orbit under such a force would have its orbital speed v proportional to

(A)

^{1}/R^{2}

(B)

R^{0}

(C)

R

(D)

^{1}/R

Question-2

A second pendulum is mounted in a rocket. Its period of oscillation decreases when the rocket

(A)

Comes down with uniform acceleration

(B)

Moves round the earth in a geostationary orbit

(C)

Moves up with a uniform velocity

(D)

Moves up with uniform acceleration

Question-3

A satellite A of mass m is at a distance r from the surface of the earth. Another satellite B of mass 2m is at a distance of 2r from the earth's surface. Their time periods are in the ratio of

(A)

1 : 2

(B)

1 : 16

(C)

1 : 32

(D)

1 : 2√2

Question-4

The escape velocity of a sphere of mass m is given by (G = universal gravitational constant, M_{e} = mass of earth and Re = radius of earth)

(A)

(B)

(C)

(D)

Question-5

For a satellite escape velocity is 11 km/s. If the satellite is launched at an angle of 60^{o} with the vertical, then escape velocity will be

(A)

11 Km/s

(B)

11√3 Km/s

(C)

^{11}/√3 Km/s

(D)

33 Km/s

Question-6

A ball is dropped from a satellite revolving around the earth at a height of 120km.The ball will

(A)

Continue to move with same speed along a straight line tangentially to the satellite at that time

(B)

Continue to move with the same speed along the original orbit of satellite

(C)

Fall down to earth gradually

(D)

Go far away in space

Question-7

A body of mass m is placed on earth's surface. It is then taken from earth's surface to a height h = 3R, then the change in gravitational potential energy is

(A)

^{mgh}/R

(B)

^{2}/3 mgR

(C)

^{3}/4 mgR

(D)

^{mgR}/2

Question-8

The escape velocity from earth is 11.2 km/s. If a body is to be projected in a direction making an angle 45^{o} to the vertical, then the escape velocity is

(A)

11.2 × 2 km/s

(B)

11.2 km/s

(C)

11.2/√2 km/s

(D)

11.2√2 km/s

Question-9

The satellite of mass m is orbiting around the earth in a circular orbit with a velocity v. What will be its total energy?

(A)

3/4 mv^{2}

(B)

^{1}/2 mv^{2}

(C)

mv^{2}

(D)

- (^{1}/2)mv^{2}

Question-10

The mean radius of earth is R, its angular speed on its own axis is ω and the acceleration due to gravity at earth's surface is g. What will be the radius of the orbit of a geostationary satellite?

(A)

(B)

(C)

(D)

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