Calculate the average density of the earth in terms of $g$, $G$ and $R$.

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 packet, dropped from a stationary helicopter, hovering at a height  $\text{'}h\text{'}$ from the ground level, reaches the ground in $12 \text{s}$.  Calculate

(i) The value of $h$   

(ii) The final velocity of the packet on reaching the ground. 

($\mathrm{Take} g=9.8 \mathrm{m} {\mathrm{s}}^{-2}$)

A boy drops a stone from a cliff, which reaches the ground in $8 \text{s}$. Calculate

(i) the final velocity of the stone,

(ii) the height of the cliff. 

($\mathrm{Take} \mathrm{g}=9.8 \raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{s}}^2$}\right.$)

To estimate the height of a bridge over a river, a stone is dropped from the bridge. It takes $3$ seconds to touch the surface of water. Calculate the height of the bridge and the velocity with which it hits the surface of water. [Take $g=9.8 \raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{s}}^2$}\right.$].

A stone dropped from a cliff on the surface of the Moon, reaches the surface of the moon in $30 \text{s}$. If the acceleration due to gravity of the moon is $1.63 \raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{s}}^2$}\right.$ . Calculate

(i) the height of the cliff,

(ii) the velocity of the stone on touching the surface of the Moon.

A stone thrown vertically upward takes $3 \text{s}$ to attain the maximum height. Calculate,

(i) the initial velocity of the stone.

(ii) the maximum height attained by the stone.

(Take $g=9.8 \raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{s}}^2$}\right.$)