Question

(a) Identical packets are dropped from two aeroplanes, one above the equator and the other above the north pole, both at height $h$. Assuming all conditions are identical, will these packets take same time to reach the surface of the earth? Justify your answer.
(b) It is seen that a falling apple is attracted towards the earth. Does the apple also attract the earth? If so, we do not see the earth moving towards the apple. Why?

Answer 1

(a) No, those packets do not take same time to reach the surface of earth. The earth is not a perfect sphere. As the radius of the earth increases from the poles to the equator, the value of 'g' becomes greater at the poles than at the equator. Therefore, the packet falls slowly at the equator in comparison to the poles. Thus, the packet will remain in air for longer time interval, when it is dropped at the equator.
(b) According to the third law of motion, the apple does attract the earth. But according to the second law of motion, for a given force, acceleration is inversely proportional to the mass of an object. The mass of an apple is negligibly small compared to that of the earth. So, we do not see the earth moving towards the apple.

$m_a{g}_a=m_E{g}_E$.

As the mass of the apple is negligible when compared to the mass of earth, the acceleration produced in the apple will be much greater than that produced in the earth.