Question

An astronaut named Alex is exploring a newly discovered planet, Xylon, which has a mass of 5 × 10²⁴ kg and a radius of 6,400 km. Alex, with a mass of 80 kg, is on the surface of Planet Xylon. The planet is unique because it has only one-sixth of the density of Earth but the same surface gravity.

With the help of Second Law of Motion and the Universal Law of Gravitation derive an expression for acceleration due to gravity 'g'.

The weight of any person on the moon is about 1/6 times that on the earth. He can lift a mass of 15 kg on the earth. What will be the maximum, mass, which can be lifted by the same force applied by the person on the moon?

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.