If the distance between the centres of Earth and Moon is $D$ and mass of Earth is $81\, times$ that of Moon. At what distance from the centre of Earth gravitational field will be zero?

Two identical spheres are placed in contact with each other. The force of gravitation between the spheres will be proportional to ($R =$ radius of each sphere)

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

If the acceleration due to gravity at earth is $'g'$ and mass of earth is $80$ times that of moon and radius of earth is $4$ times that of moon, the value of acceleration due to gravity at the surface of moon will be

If the radius of the earth were to shrink by $1\%$ its mass remaining the same, the acceleration due to gravity on the earth's surface would

If $M$ is mass of a planet and $R$ is its radius then in order to become black hole [ $c$ is speed of light]