Question

i) Derive the formula for the gravitational force using the factors on which it

depends ?

ii) 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?​

Answer 1

Answer:

We know that according to Newton's law of gravitation, all objects in the universe attract each other.

F is directly proportional to masses of the two objects.......(i)

F is inversely proportional to the distance between the two objects......(ii)

From (i) and (ii) we can say that F is directly proportional to mass of two objects/the square of distance between them.

We know that in order to change a proportionate sign to equal to sign, we need to add a constant {[Here, G]}

=> F= Gm1m2/r^2(where m1 and m2 are the masses of two objects and r is thedistance between them.)

When diameter of earth becomes half, its radius R also become half, its radius R also become half i.e.,R′=R/2 and its mass becomes four times i.e.,M′=4M. i.e., the weight of the same object would become 16 times its original weight.

Explanation: