When a spaceship is two earth radii distant from the centre of the earth,its gravitational acceleration is: (in $, m s^{-2}$)

Give a reason for the statement that the value of $g$ is greater at the poles than at the equator.

What is the magnitude of the gravitational force between the earth and a $1 \,kg$ object on its surface (in $,N$)? (Mass of the earth is $6 \times 10^{24} \,kg$ and radius of the earth is $6.4 \times 10^6 \,m$.)

Two objects of masses $m_1$ and $m_2$ having the same size are dropped simultaneously from heights $h_1$ and $h_2$ respectively. Find out the ratio of time they would take in reaching the ground. Will this ratio remain the same if $(i)$ one of the objects is hollow and the other one is solid and $(ii)$ both of them are hollow,size remaining the same in each case. Give reason.

$A$ ball thrown up vertically returns to the thrower after $6 \, s$. Find:
$(a)$ The velocity with which it was thrown up.
$(b)$ The maximum height attained. (Take $g = 9.8 \, m s^{-2}$)

$A$ stone is dropped from a cliff. Its speed after it has fallen $100 \,m$ is: (in $, m s^{-1}$)