If \(A\) is the areal velocity of a planet of mass \(M,\) then its angular momentum is:

1.	\(\frac{M}{A}\)	2.	\(2MA\)
3.	\(A^2M\)	4.	\(AM^2\)

Magnitude of potential energy (U) and time period (T) of a satellite are related to each other as:

1. $T^2$ $\alpha$ $\frac{1}{U^3}$

2. $T$ $\alpha$ $\frac{1}{U^3}$

3. $T^2$ $\alpha$ $U^3$

4. $T^2$ $\alpha$ $\frac{1}{U^2}$

A projectile is fired upwards from the surface of the earth with a velocity ${\mathrm{kv}}_{\mathrm{e}}$ where ${\mathrm{v}}_{\mathrm{e}}$ is the escape velocity and k < 1. If r is the maximum distance from the center of the earth to which it rises and R is the radius of the earth, then r equals:
1. \(\frac{R}{k^2}\)

2. \(\frac{R}{1-k^2}\)

3. \(\frac{2R}{1-k^2}\)

4. \(\frac{2R}{1+k^2}\)

For the moon to cease as the earth's satellite, its orbital velocity has to be increased by a factor of -

A rocket of mass M is launched vertically from the surface of the earth with an initial speed v. Assuming the radius of the earth to be R and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is   

1. $\mathrm{R}/\left(\frac{\mathrm{gR}}{2{\mathrm{v}}^2}-1\right)$                         

2. $\mathrm{R}\left(\frac{\mathrm{gR}}{2{\mathrm{v}}^2}-1\right)$

3. $\mathrm{R}/\left(\frac{2\mathrm{gR}}{{\mathrm{v}}^2}-1\right)$                         

4. $\mathrm{R}\left(\frac{2\mathrm{gR}}{{\mathrm{v}}^2}-1\right)$

If two planets are at mean distances $d_1$ and $d_2$ from the sun and their frequencies are n₁ and n₂ respectively, then:

1. ${n_1}^2{d_1}^2=n_2{d_2}^2$                                 

2. ${n_2}^2{d_2}^3={n_1}^2{d_1}^3$

3. $n_1{d_1}^2=n_2{d_2}^2$                                   

4. ${n_1}^2{d}_1={n_2}^2{d}_2$

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.  ${\left(\frac{R_A}{R_B}\right)}^2$

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

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. \(1/R\)