The pair of physical quantities that are scalar only are ?

Step 1: Analyze the question We need the pair in which both quantities are scalars, meaning they have magnitude only and no direction.

Step 2: Recall the concept

• Scalar: magnitude only (e.g. mass, time, speed, volume, area, length, energy)
• Vector: magnitude and direction (e.g. displacement, velocity, force, momentum, impulse, moment of a force in some treatments)

Step 3: Check each option

• A. Volume and area: Volume is the space occupied by a body, so it is a scalar. Area is the size of a surface, so it is also a scalar (in basic secondary-school physics). Both are scalars.
• B. Moment and momentum: Momentum = mass × velocity, so it is a vector. The moment of a force (torque) has a turning direction, clockwise or anticlockwise. Not scalar only.
• C. Length and displacement: Length is a scalar, but displacement is a vector. Not scalar only.
• D. Impulse and time: Time is a scalar, but impulse = force × time, which has the direction of the force, so it is a vector. Not scalar only.

Step 3 result: Only option A has two quantities that are both scalars.

Answer: A. volume and area

Exam tip: To spot a vector, ask whether you must say "in which direction?" A vector needs a direction (displacement, velocity, force, momentum, impulse). Anything you can describe with just a number and a unit (volume, area, length, time, mass, energy) is a scalar. In "which pair is scalar only" questions, eliminate any option that contains a known vector, such as displacement, momentum or impulse.