Suppose the law of gravitational attraction suddenly changes and becomes an inverse cube law i.e., $F\propto 1/r^3$ but the force still remains a central force, then:

1.	Kepler's law of areas still holds
2.	Kepler's law of period still holds
3.	Kepler's law of areas and period still hold
4.	Neither the law of areas nor the law of period still hold

The distance of a planet from the sun is \(5\) times the distance between the earth and the sun. The time period of the planet is: 

Two satellites A and B go around the earth in circular orbits at heights of ${\mathrm{R}}_{\mathrm{A}} \mathrm{and} {\mathrm{R}}_{\mathrm{B}}$ respectively from the surface of the earth. Assuming earth to be a uniform sphere of radius $R_e$, the ratio of the magnitudes of their orbital velocities is:

1.  $\sqrt{\frac{R_B}{R_A}}$

2.  $\frac{R_B+R_e}{R_A+R_e}$

3.  $\sqrt{\frac{R_B+R_e}{R_A+R_e}}$

4.  ${\left(\frac{R_A}{R_B}\right)}^2$

The orbital angular momentum of a satellite revolving at a distance \(r\)from the centre is \(L\). If the distance is increased to 16r, then the new angular momentum will be:

A body of mass m kg starts falling from a point 2R above the Earth’s surface. Its kinetic energy when it has fallen to a point ‘R’ above the Earth’s surface, is:
[R - Radius of Earth, M - Mass of Earth, G - Gravitational Constant] -

1. $\frac{1}{2}\frac{GMm}{R}$              

2. $\frac{1}{6}\frac{GMm}{R}$

3. $\frac{2}{3}\frac{GMm}{R}$               

4. $\frac{1}{3}\frac{GMm}{R}$

A body is projected vertically upwards from the surface of a planet of radius R with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is:

1.  R/3                            

2.  R/2

3.  R/4                            

4.  R/5

A satellite is launched into a circular orbit of radius R around the Earth while a second satellite is launched into an orbit of radius 1.02R. The percentage difference in the time periods of the two satellites is: 

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

1. $1/R^2$                        

2. $R^{\circ }$

3. $R^1$                             

4. \(1/R\)

If the acceleration due to gravity at a height 1 km above the earth is similar to a depth d below the surface of the earth, then: 

1. d=0.5 km

2. d=1 km

3. d=1.5 km

4. d=2 km

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