How does the weight of an object vary with respect to mass and radius of the earth. In a hypothetical case, if the diameter of the earth becomes half of its present value and its mass becomes four times of its present value, then how would the weight of any object on the surface of the earth be affected?

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

The earth is acted upon by gravitation of Sun, even though it does not fall into the Sun. Why?

How does the force of attraction between the two bodies depend upon their masses and 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.

Two objects of masses m ₁ and m₂ having the same size are dropped simultaneously from heights h₁ and h₂ 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.