Match the $\text{LIST-I}$ with $\text{LIST-II}$:

$\text{LIST-I}$	$\text{LIST-II}$
$A$. Gravitational constant	$I$. $[LT^{-2}]$
$B$. Gravitational potential energy	$II$. $[L^2 T^{-2}]$
$C$. Gravitational potential	$III$. $[ML^2 T^{-2}]$
$D$. Acceleration due to gravity	$IV$. $[M^{-1} L^3 T^{-2}]$

Choose the correct answer from the options given below:

Suppose the acceleration due to gravity at the earth's surface is $10 \, m/s^2$ and at the surface of Mars it is $4.0 \, m/s^2$. $A$ $60 \, kg$ passenger travels from the Earth to Mars in a spaceship moving with a constant velocity. Neglect all other objects in the sky. Which curve in the figure best represents the weight (net gravitational force) of the passenger as a function of time?

The figure shows the orbit of a planet $P$ around the sun $S.$ $AB$ and $CD$ are the minor and major axes of the ellipse,respectively. If $U$ is the potential energy and $K$ is the kinetic energy of the planet,then $|U| > |K|$ at:

$A$ particle of mass $m$ is dropped from a height $R$ equal to the radius of the earth above the tunnel dug through the earth as shown in the figure. Hence the correct statement is

Fill in the blanks:
$(a)$ The orbital period of Mars around the Sun is $8$ times the orbital period of Mercury. If the distance of Mercury from the Sun is $5.79 \times 10^{10} \, m$,then the distance of Mars from the Sun is approximately .......
$(b)$ If the mass of an object on Earth is $m \, kg$,then the mass of the same object on the Moon is ........... .
$(c)$ The height of a geostationary satellite from the Earth's surface is approximately ........ .
$(d)$ If the distance between two objects of mass $m_1 = m_2 = 1 \, kg$ is $1 \, mm$,then the magnitude of the gravitational force between them is ........... . $[G = 6.67 \times 10^{-11} \, SI \text{ units}]$

The radius and mass of the Earth are both increased by $0.5\%$. Which of the following statements is true at the surface of the Earth?