The earth takes $24\; h$ to rotate once about its axis. How much time (in $min$) does the sun take to shift by $1^o$ when viewed from the earth?

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 ............ .

$A$ 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

$A$ body of mass $m$ is moving in a circular orbit of radius $R$ about a planet of mass $M$. At some instant,it splits into two equal masses. The first mass moves in a circular orbit of radius $\frac{R}{2}$,and the other mass moves in a circular orbit of radius $\frac{3R}{2}$. The difference between the final and initial total energies is

For a satellite to orbit around the earth,which of the following must be true?

Statement $(A)$ Two artificial satellites revolving in the same circular orbit have the same period of revolution.
Statement $(B)$ The orbital velocity is inversely proportional to the square root of the radius of the orbit.
Statement $(C)$ The escape velocity of a body is independent of the altitude of the point of projection.