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.
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.
$(a)$ False : Despite being a scalar quantity, energy is not conserved in inelastic collisions.
$(b)$ False : Despite being a scalar quantity, temperature can take negative values.
$(c)$ False : Total path length is a scalar quantity. Yet it has the dimension of length.
$(d)$ False : A scalar quantity such as gravitational potential can vary from one point to another in space.
$(e)$ True : The value of a scalar does not vary for observers with different orientations of axes.
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