The dependence of the intensity of the gravitational field $(E)$ of the Earth on the distance $(r)$ from the center of the Earth is correctly represented by:

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?

$A$ particle of mass $M$ is situated at the centre of a spherical shell of same mass $M$ and radius $a$. The gravitational potential at a point situated at a distance of $\frac{a}{2}$ from the centre will be:

$A$ star of mass $M$ and radius $R$ is made up of gases. The average gravitational pressure compressing the star due to the gravitational pull of the gases making up the star depends on $R$ as

$A$ particle of mass $m$ having negative charge $q$ moves along an ellipse around a fixed positive charge $Q$ such that its maximum and minimum distances from the fixed charge are $r_1$ and $r_2$ respectively. The angular momentum $L$ of this particle is:

Fill in the blanks:
$(a)$ In the region inside the Earth,the acceleration due to gravity is proportional to the distance from the center of the Earth as ..... .
$(b)$ If the Earth shrinks such that its radius becomes half and its mass remains constant,the weight of an object on the Earth increases by a factor of ......... .
$(c)$ The orbital velocity of a geostationary satellite of the Earth is approximately ............ .