# Weight

The weight of a body on the earth is defined as "the force with which it is attracted by the earth". The weight (W) of a body of mass 'm' on the surface of the earth is given by the law of gravitation, i.e.Â Â Â -----------(1.2)

where, M is the mass of the earth and R its radius. We know that the value of acceleration due to gravity is

Thus, the weight of a body on the earth is also given by

W = mgÂ Â Â Â Â Â Â Â Â Â Â Â Â Â ------------(1.3)

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To keep a body from falling, one has to exert on it an upward force equal to its weight W so as to make the total force equal to zero. The body remains at rest because the two forces act on it - the downward pull of its weight and the upward pull of the string-add up to zero. If the pull of the string is removed the body would be accelerated downwards under the action of a single force, mg. The fact that a freely falling body moves with a constant acceleration, g, and independent of its speed implies that this downward force is always present whether the body is moving or not.

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Mass and weight are different quantities. Mass is the quantity of matter contained in a body. By definition, the mass of a given object is the same anywhere in the universe.

Weight is the force with which a body is attracted by the earth. The weight W of a body and its mass m are related as W = mg

where, g is the acceleration due to gravity and is given by g = GM/R^{2}.

Now g is inversely proportional to the square of the distance. Hence, g is less on a mountain than at sea level, though only slightly smaller. Thus, weight changes from place to place.

**Mass and Weight**