Match List-$I$ with List-$II$:

$(a)$ Gravitational constant $(G)$	$(i)$ $[L^{2}T^{-2}]$
$(b)$ Gravitational potential energy	$(ii)$ $[M^{-1}L^{3}T^{-2}]$
$(c)$ Gravitational potential	$(iii)$ $[LT^{-2}]$
$(d)$ Gravitational intensity	$(iv)$ $[ML^{2}T^{-2}]$

Choose the correct answer from the options given below:

Three particles,each of mass $M$,are situated at the vertices of an equilateral triangle of side length $L$. The only forces acting on the particles are their mutual gravitational forces. It is desired that each particle moves in a circle while maintaining the original separation $L$. The initial speed that should be given to each particle is

$A$ spherical hole of radius $R/2$ is excavated from an asteroid of mass $M$ and radius $R$,as shown in the figure. The gravitational acceleration at a point on the surface of the asteroid just above the excavation is:

Match the column $-I$ with column $-II$ for a satellite in circular orbit:

Column $-I$	Column $-II$
$(A)$ Kinetic energy	$(p)$ $-\frac{GM_Em}{2r}$
$(B)$ Potential energy	$(q)$ $\sqrt{\frac{GM_E}{r}}$
$(C)$ Total energy	$(r)$ $-\frac{GM_Em}{r}$
$(D)$ Orbital velocity	$(s)$ $\frac{GM_Em}{2r}$

(where $M_E$ is the mass of the earth,$m$ is the mass of the satellite,and $r$ is the radius of the orbit)

Every planet revolves around the sun in an elliptical orbit. Which of the following statements are correct?
$A.$ The force acting on a planet is inversely proportional to the square of the distance from the sun.
$B.$ The force acting on the planet is inversely proportional to the product of the masses of the planet and the sun.
$C.$ The centripetal force acting on the planet is directed away from the sun.
$D.$ The square of the time period of revolution of a planet around the sun is directly proportional to the cube of the semi-major axis of the elliptical orbit.
Choose the correct answer from the options given below:

$A$ planet is moving in an elliptical orbit around the sun. The work done on the planet by the gravitational force of the sun:
$(i)$ is zero in no part of the motion.
(ii) is zero in some parts of the orbit.
(iii) is zero in one complete revolution.
(iv) is zero in any small part of the orbit.
Which of the following is true?