Gravitation

The height at which the acceleration due to gravity becomes g/9

The height at which the acceleration due to gravity becomes g/9 (where g = the acceleration due to gravity on the surface of the earth) in terms of R, the radius of the earth, is

(√2)R
R/2
R/√2
2R

Two bodies of masses m and 4m are placed at a distance r

Two bodies of masses m and 4m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is

zero
-4Gm/r
-6Gm/r
-9Gm/r

If suddenly the gravitational force of attraction between Earth

If suddenly the gravitational force of attraction between Earth and a satellite revolving around it becomes zero, then the satellite will

move tangentially to the originally orbit in the same velocity
continue to move in its orbit with same velocity
become stationary in its orbit
move towards the earth

The escape velocity for a body projected vertically upwards

The escape velocity for a body projected vertically upwards from the surface of earth is 11 km/s. If the body is projected at an angle of 45° with the vertical, the escape velocity will be

11/√2 m/s
11√2 km/s
22 km/s
11 km/s

The kinetic energy needed to project a body of mass

The kinetic energy needed to project a body of mass m from the earth surface (radius R) to infinity is

mgR
2mgR
mgR/4
mgR/2

The escape velocity of a body depends upon mass as

m⁰
m¹
m²
m³

The mass of a spaceship is 1000 kg. It is to be launched

The mass of a spaceship is 1000 kg. It is to be launched from the earth's surface out into free space. The value of 'g' and 'R' (radius of earth) are 10 m/s² and 6400 km respectively. The required energy for this work will be

6.4 X 10⁸ Joules
6.4 X 10⁹ Joules
6.4 X 10¹⁰ Joules
6.4 X 10¹¹ Joules

Energy required to move a body of mass m from an orbit of radius 2R to 3R

Energy required to move a body of mass m from an orbit of radius 2R to 3R is

(GMm)/(3R²)
(GMm)/(6R)
(GMm)/(8R)
(GMm)/(12R²)

A very long (length L) cylindrical galaxy is made of uniformly distributed mass and has radius R

A very long (length L) cylindrical galaxy is made of uniformly distributed mass and has radius R (R<<L). A star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing through its centre. If the time period of star is T and its distance from the galaxy's axis is r, then:

T² ∝ r³
T ∝ r²
T ∝ r
T ∝ √r