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.
