# How to differentiate between mass and weight? [duplicate]

Today while solving numericals in my physics book I got struck over a question which said "A hammer weighing 1kg .....". In the question they told that the weight of hammer is 1 Kg but when i checked in hints or solution the same question on the net, i saw that they had used 1 kg as the mass of the hammer. So how can we determine if the question is referring to mass or weight of an object?

Mass $$m$$ is a measure of the amount of matter in an object. It is usually expressed in $$\mathrm{kg}$$ ($$\text{kilogram}$$).

Weight $$W$$ is the force the Earth's gravitational field exerts on a mass $$m$$. It is usually expressed in $$\mathrm{N}$$ ($$\text{Newton}$$) and is obtained as follows: $$W=m\times g$$ where $$g$$ is the Earth's gravitational acceleration, $$\text{9.81}\mathrm{m/s^2}$$ (for objects relatively close to the Earth's surface).

"A hammer weighing 1kg .....".

is therefore a slightly confusing way of putting things.

"A hammer of mass $$1\mathrm{kg..."}$$

would be a better way of putting it. However, the fact that the text referred to $$\mathrm{kg}$$ is a strong indication that the author was referring to mass, not weight.

• But it can also be that the author is refering to gravitational unit of force i.e Kg wt ( Kilogram Weight ) – Tushar Nov 8 '19 at 23:13
• Yes, but it is rarely used now and should be explicitly stated, as *kilogram force". You only find it in older engineering books now. – Gert Nov 8 '19 at 23:15

In common parlance the words weight and mass are regarded as synonyms although they are different properties relating to an object. The act of finding the mass of an object is called weighing and not massing.

So you need to think about the context and also look at the units.
You will find the kilogram-force, which is approximately $$9.8\,\rm N$$, used as a unit of weight.
Even then you need to be careful as the imperial unit of mass, the pound, can be found to be used as a unit of force/weight.

As to the question you are referring I think that a phrase of the type “weighing $$1\,\rm kg$$” will invariably be referring to mass.

The difference in weight and mass is that mass refers to an amount of material while weight is a force caused by the gravitation attraction of the earth in this case. So a 1 kg hammer weighs 1 kg x 9.8 $$\frac{m}{sec^2}$$ = 9.8 N.

It should be noted that on another planet or say the moon the hammer will still have a mass of 1 kg but its weight will be much less because the acceleration due to gravity is much less than 9.8. The mass is an inherent property of an object while the weight is due to the gravitation attraction between the object and the place that it occupies.