Scalars and Vectors: (May - June 2003 Paper 1 Question No. 08)

Which of the following groups of physical quantities consists only of scalars?

A acceleration, force, velocity

B acceleration, mass, speed

C force, time, velocity

D mass, speed, time

Correct Answer: D

Explanation:

Scalars are the physical quantities which have only a magnitude (value) but no direction is associated with them. On the other hand, Vectors are the quantities which have a magnitude as well as a direction. Another basic rule about vector and scalar is if we multiply a vector with a scalar it will be a vector, if we multiply a vector with another vector then the result might be a scalar or a vector which can be found by cross multiplication of the vectors (cross multiplication is beyond the O level syllabus and hence its avoided here) and if we multiply a scalar with another scalar it will be a scalar but if we multiply a scalar with a vector then it will be a vector. Briefly we can say:

Scalar x Scalar = Scalar

Scalar x Vector = Vector

Vector x Scalar = Vector

Vector x Vector = Scalar or Vector

So, according to the definition above we can see:

A: acceleration is a vector as it is the rate of change of velocity which itself is a vector. Velocity has a direction and a magnitude. Then force is a vector which is defined as, Force = (mass x acceleration). Here acceleration is a vector. Velocity is also a vector as it’s the speed of an object toward a particular direction.

B: Acceleration → vector, mass → scalar (it has no direction), speed → scalar (no direction)

C: Force → vector, time → scalar, velocity → vector

D: mass → scalar, speed → scalar, time → scalar.

So, correct answer is D where all the quantities are scalars.

O Level Physics

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