If the density of a planet is doubled without changing its radius,how does $g$ on the planet change?

State whether the following statement is True or False:
All objects attract each other along the line joining their centre of mass.

An apple falls from a tree because of gravitational attraction between the earth and the apple. If $F_1$ is the magnitude of force exerted by the earth on the apple and $F_2$ is the magnitude of force exerted by the apple on the earth,then:

$(i)$ Seema buys a few grains of gold at the poles as per the instructions of one of her friends. She hands over the same when she meets her at the equator. Will the friend agree with the weight of gold bought? If not,why?
$(ii)$ If the moon attracts the earth,why does the earth not move towards the moon?

Which of the following is the evidence to show that there must be a force acting on the earth and directed towards the sun?

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.