Read each statement below carefully and state, with reasons and examples, if it is true or false :
A scalar quantity is one that ;
(a) is conserved in a process.
(b) can never take negative values

(c) must be dimensionless.

(d) does not vary from one point to another in space.
(e) has the same value for observers with different orientations of axes.

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Solution

(a) False: Scalars need not be constant. Example: distance travelled by a moving object.
(b) Scalars can be positive as well as negative, for eg. Temperature can be -20 deg Celsius. Hence, above statement is false.

(c) Scalar quantities have dimensions, they do not have directions. Distance is scalar and has dimension. Hence, it is a false statement.

(d) False: A scalar quantity such as gravitational potential can vary from one point to another in space.
(e) Scalar quantity does not vary with axes, hence the above statement is true.

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