Where will a body weigh more: $1 \, km$ above the surface of the earth or $1 \, km$ below the surface of the earth?

How does the force of attraction between two bodies depend upon their masses and the distance between them? $A$ student thought that two bricks tied together would fall faster than a single one under the action of gravity. Do you agree with his hypothesis or not? Comment.

Calculate the force of gravitation between two objects of masses $10 \; kg$ and $20 \; kg$ at a distance of $10 \; m$ from each other. $\left[G = 6.67 \times 10^{-11} \; Nm^2 kg^{-2}\right]$

Prove that if a body is thrown vertically upward,the time of ascent is equal to the time of descent.

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.

Show that the weight of an object on the moon is one-sixth of its weight on the earth. [Given: mass of earth $= 5.98 \times 10^{24} \ kg$,mass of moon $= 7.36 \times 10^{22} \ kg$,radius of earth $= 6.37 \times 10^{6} \ m$,radius of moon $= 1.74 \times 10^{6} \ m$]