The dependence of acceleration due to gravity $'g'$ on the distance $'r'$ from the centre of the earth, assumed to be a sphere of radius $R$ of uniform density is as shown in figure below

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

$Assertion$ : The escape speed does not depend on the direction in which the projectile is fired.
$Reason$ : Attaining the escape speed is easier if a projectile is fired in the direction the launch site is moving as the earth rotates about its axis.

A body tied to a string of length $L$ is revolved in a vertical circle with minimum velocity, when the body reaches the upper most point the string breaks and the body moves under the influence of the gravitational field of earth along a parabolic path. The horizontal range $AC$ of the body will be

The mass of planet is $\frac{1}{9}$ of the mass of the earth and its radius is half that of the earth. If a body weight $9\,N$ on the earth. Its weight on the planet would be  ........ $N$

Two spheres of masses $m$ and $M$ are situated in air and the gravitational force between them is $F$ . the space around the masses is now filled with a liquid of specific gravity $3$ . The gravitational force between bodies will now be