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

The figure shows the elliptical orbit of a planet $m$ about the sun ${S}.$ The shaded area $SCD$ is twice the shaded area $SAB.$ If $t_1$ is the time for the planet to move from $C$ to $D$ and $t_2$ is the time to move from $A$ to $B,$ then:
                     

Let the speed of the planet at the perihelion $P$ in figure shown below be $v_{_P}$ and the Sun-planet distance $\mathrm{SP}$ be $r_{_P}.$ Relation between $(r_{_P},~v_{_P})$ to the corresponding quantities at the aphelion $(r_{_A},~v_{_A})$ is:

Which of the following quantities remain constant in a planetary motion (consider elliptical orbits) as seen from the sun?

Two planets orbit a star in circular paths with radii $R$ and $4R,$ respectively. At a specific time, the two planets and the star are aligned in a straight line. If the orbital period of the planet closest to the star is $T,$ what is the minimum time after which the star and the planets will again be aligned in a straight line?

Three equal masses of $m$ kg each are fixed at the vertices of an equilateral triangle $ABC.$ What is the force acting on a mass $2m$ placed at the centroid $G$ of the triangle? 
(Take $AG=BG=CG=1$ m.)

       

1. $Gm^2(\hat{i}+\hat{j})$
2. $Gm^2(\hat{i}-\hat{j})$
3. zero
4. $2Gm^2(\hat{i}+\hat{j})$

Two spheres of masses $m$ and $M$ are situated in air and the gravitational force between them is $F.$ If the space around the masses is filled with a liquid of specific density $3,$ the gravitational force will become:
1. $3F$
2. $F$
3. $F/3$
4. $F/9$

If a particle is projected vertically upward with a speed $u,$ and rises to a maximum altitude $h$ above the earth's surface then:
($g=$ acceleration due to gravity at the surface)