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Last updated date: 09th Dec 2023
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MVSAT Dec 2023

Can a scalar be negative ?

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Hint: Here, we are asked about the negativity property of a scalar, is it possible or not. Now, in order to answer this question, what you need to do is understand exactly what a scalar is, then think of quantities that are assigned in the category of scalar and comment on the signs which the quantities can take.

Complete answer:
A scalar quantity is a quantity which has magnitude and nothing else, by nothing else what is meant is that it has no other properties such as direction. It is just a number having some value which determines the magnitude of a certain quantity. The range of scalar quantity is the whole number line, but that scalar quantity takes only one value from the whole number line, that is the real number category. Now, as the real numbers include both, positive numbers as well as negative numbers, a scalar can be negative. Now, in physics, the magnitude of a physical quantity is expressed by some magnitude or say numerical value and a unit.

Now, if you consider a force acting on a block, you can see that the force will have some magnitude but in addition to it, it will also have a direction. For example, a force of 5N is acting on the block in the x-direction, so clearly force is not a scalar quantity. Now, consider the work done which is equal to the dot product of force and displacement. You know that dot product gives a numerical value, this numerical value is scalar. Now, work is actually energy, so energy is a scalar quantity. Energy can take both, positive as well as negative values. So, now you can comment on scalar that it can be negative.

Therefore, a scalar can be negative.

Note:We have discussed in brief about scalar. Remember that the scalar can take any value that belongs to real numbers which means that the scalar can be positive, negative, rational and as well as irrational. Also, remember that scalars are used to express magnitude of physical quantities such as pressure and energy.