Measurement of Weight

Everything is attracted to the earth with a certain force and this force depends on the mass (m) of the object and the acceleration due to gravity (g).

The Force on any object of mass m which is moving with acceleration a can be expressed as,

F = m × a

As all objects experience acceleration due to gravity on the Earth,

F = m × g

The weight of an object is defined as the earth’s force of attraction on it and it is represented by W. 

W = m × g

The weight is a downward-acting force that has both magnitude and direction so, it is a vector quantity. 

Weight on Earth

The earth’s shape looks spherical, but it is an unevenly shaped ellipsoid. The distance between a point at the equator and the centre of the earth is more than the distance between the point at the North Pole and the centre of the earth. From the expression,

• g = GM/R²
• W = mg

It is observed that acceleration due to gravity (g) is inversely proportional to the square of the distance between the object and the earth, an object placed at the North Pole would have more weight than the weight at the equator. Therefore, as the mass remains constant but the acceleration due to gravity varies from place to place, the weight of an object can also vary from place to place on the earth’s surface.

Weight on Moon

The weight of an object on the Earth is the force with which the earth attracts the object. Similarly, the weight of an object on the moon is the force that attracts that object to the moon. The moon has a mass that is less than that of the Earth. As a result, the moon has less attraction to objects i.e., approximately (1/6)^th of the Earth’s force of attraction. Thus weight on the moon is (1/6)^th of the weight on Earth.

Mass and Weight are commonly used in the same manner by the general masses but there are differences between both Mass and Weight, where Mass is the measure of Inertia unlike Weight which is a measure of force acting on a body towards the heavy body. But yet still many people use these two terms interchangeably.

As we know that to change the speed or direction of an object, a force is required. If you drop anything from a great height, it will fall towards the earth’s surface. The planet revolves around the Sun and the moon revolves around the earth. There must be some force operating on objects, planets, and other celestial bodies. Isaac Newton noted that the same force is responsible for all these. This force is called gravitational force.