Read each statement below carefully and state, with reasons and examples, if it is true or false: A scalar quantity is one that
is conserved in a process
False. A scalar quantity need not be conserved in a process. For example, temperature is a scalar but is not conserved—it can increase or decrease during heating or cooling. Similarly, speed is a scalar that changes during accelerated motion.
can never take negative values
False. A scalar quantity can take negative values. For example, temperature can be negative (below 0°C). Work is another scalar that can be negative when the force and displacement are oppositely directed.
must be dimensionless
False. A scalar quantity need not be dimensionless. As stated in the context, a scalar is specified by a single number with the proper unit. Mass has dimensions [M], distance has dimensions [L], and time has dimensions [T].
does not vary from one point to another in space
False. A scalar quantity can vary from one point to another in space. For example, temperature varies from place to place and at different altitudes. Pressure is another scalar that varies with height.
has the same value for observers with different orientations of axes.
True. A scalar quantity has the same value for observers with different orientations of axes. This is because a scalar is specified completely by a single number with proper unit and has no direction associated with it. For example, the mass of an object remains the same regardless of how the coordinate axes are oriented.
Explanation
This question tests the fundamental understanding of scalar quantities. The key definition from the textbook states that 'A scalar quantity is a quantity with magnitude only. It is specified completely by a single number, along with the proper unit.' Only statement (e) correctly describes this property - scalars are independent of coordinate orientation. Statements (a) through (d) incorrectly attribute properties to scalars that are not defining characteristics.