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

Time period of simple pendulum increases by an amount $\sqrt 2 $ times at height $'h'$ from the surface of earth. Then the value of $h$ is

The magnitudes of gravitational field at distances $r_1$ and $r_2$ from the centre of a uniform sphere of radius $R$ and mass $M$ are $F_1$ and $F_2$ respectively. Then-

Two spherical bodies of mass $M$ and $5M$ and radii $R$ and $2R$ respectively are released in free space with initial separation between their centres equal to $12\,R$. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is

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

Three identical bodies of equal mass $M$ each are moving along a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each body is