Question

Read each statement below carefully and state, with reasons and examples, if it is true or false:

A) A scalar quantity is one that is conserved in a process.

B) A scalar quantity is one that can never take negative values.

C) A scalar quantity is one that must be dimensionless.

D) A scalar quantity is one that does not vary from one point to another in space.

E) A scalar quantity is one that has the same value for observers with different orientations of axes.

Answer 1

A) Step 1: Recall “conservation of energy” in different processes.
The statement is false.
Reason:- A scalar quantity need not be conserved in all processes.
Example:- Kinetic energy is a scalar quantity, but it is not conserved in inelastic collisions.

B) Step 1: Recall “Scalar quantity” properties.
The statement is false.
Reason: - A scalar quantity need not be always positive.
Example: - Temperature is a scalar quantity, but it can be negative.

C) Step 1: Recall some of the scalar quantities which have dimensions.
The statement is false.
Reason: - A scalar quantity need not be dimensionless.
Example: - Density is a scalar quantity but it has dimension.
Density $\left(\rho \right)=\frac{\text{mass (m)}}{\text{volume (v)}}=\frac{\left[M^1\right]}{\left[L^3\right]}$
$=\left[M^1{L}^{-3}{T}^0\right]$

D) Step 1: Recall path length/distance covered by particle.
The Statement is false
Reason: - A scalar quantity can also vary in space.
Example: - Path-length is scalar-quantity; but it varies from one point to another.


E) Step 1: Scalar quantities are independent of direction.
The statement is true.
Scalar quantity only has magnitude, so the value of a scalar does not vary for observers with different orientation of axes.
Example: - Mass is invariant for observers with different orientation of axes.