Question

Which among the following is a scalar quantity?
A. weight of a body
B. temperature gradient
C. elementary area
D. magnetic field strength.

Answer 1

Hint: Try to recall the concepts of scalar & vector quantity. Choose the option which has only magnitude & there should be no way of assigning direction to that quantity.

Complete step by step answer:
First, we should understand the term scalar & vector quantities.
- Scalar quantity: A scalar quantity is one that is specified only by its magnitude. It does not have any direction associated with it. Examples: Volume, Speed, Mass, Density, Number of moles, etc.

- Vector Quantity: A vector quantity is one that is specified by both direction & magnitude. Eg: Momentum, force, electromagnetic fields.

Now, weight is not a scalar quantity as weight of a body equals to mass × ‘g’
g = acceleration due to gravity
Weight = mg

This is the force which not only has magnitude but also direction as ‘g’ has a direction which is always downwards. So, weight is a vector quantity.
Magnetic field strength is definitely a vector quantity as it can be seen from its formula
i.e. Magnetic force = ${\text{q}}\left( {\mathop {\text{E}}\limits^ \to + \mathop {\text{V}}\limits^ \to \times \mathop {\text{B}}\limits^ \to } \right)$
which involves vectors. Hence it is a vector quantity.
Temperature on the other hand is a scalar quantity but temperature gradients always involve a direction. Naturally, temperature gradient takes place from high temperature to low temperature.
Hence it is not a scalar quantity.

Elementary area is a scalar quantity as we cannot associate any direction to it.
∴ Correct option – C Elementary area

Note: Although vectors & scalars represent different types of physical quantities, it is sometimes necessary for them to interact. While adding a scalar to a vector is impossible because of their different dimensions in space. But it is possible to multiply scalar by a vector.