# Which has more mass, a kilogram of cotton or a kilogram of iron??​

Which has more mass, a kilogram of cotton or a kilogram of iron??​

1 kg iron

Explanation:

What contributes to heaviness – mass or weight? Mass is a measurement of the amount of matter something contains, whereas Weight is the measurement of the pull of gravity on an object.

Weight varies with mass of the objects involved and the distance between their center of masses. Therefore a bowling ball will weigh less on moon than on earth because mass of earth is more than the mass of moon. We may say that iron is less heavier on moon than on earth because iron weighs less on moon than on earth. Hence its safe to conclude that Weight is what decides the “heaviness” of an object.

As per Newton’s law of gravitation: Every point mass attracts every single other point mass by a force pointing along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them:

that is : F=Gm1m2/r^2

where:

F is the force between the masses;

G is the gravitational constant (6.674×10−11 N · (m/kg)2);

m1 is the first mass;

m2 is the second mass;

r is the distance between the centers of the masses.

This force “F” is what gives an object its “heaviness”. If we were to apply this equation on an iron sphere of 1kg and a cotton sphere of 1kg placed on earth in vacuum, all the above mentioned variables are same except for the distances between the centers of the masses.

Approximate radius of iron and cotton 1 kg spheres are 6.4 cms and 14.4 cms respectively.

Since gravitational pull is inversely proportional to square of the distance between two objects, the pull of earth will be greater on iron than on cotton.

If we calculate:

earth’s gravitational force on iron=9.81964954 Newtons,

and earth’s gravitational force on cotton= 9.819649294 Newton

which means that earth exerts a tiny force of 2.5 x 10^-7 Newtons more on iron than on cotton, hence 1kg iron is heavier than 1kg cotton.

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