$A$ 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:

$A$ small ball of mass $m$ is released at a height $R$ above the earth's surface,as shown in the figure. The ball enters a narrow groove and reaches a maximum depth of $R/2$ inside the earth before coming to rest momentarily. The groove contains an ideal spring of spring constant $K$ and natural length $R$. Find the value of $K$ if $R$ is the radius of the earth and $M$ is the mass of the earth.

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

$Assertion$: Space rockets are usually launched in the equatorial line from west to east.
$Reason$: The acceleration due to gravity is minimum at the equator.

$A$ body projected vertically from the earth reaches a height equal to earth's radius before returning to the earth. The power exerted by the gravitational force is greatest

$A$ 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