Question

Which one of the following is a vector quantity?
a) Energy
b) Pressure
c) Momentum
d) Work

Answer 1

Hint: Vector quantities are those which have both magnitude and direction (direction should be specific).
So if we analyse this question, we can explain each option.

Complete step-by-step answer:
Energy: Energy is the amount of work done by a body. Work itself is a scalar quantity (see explanation below). So energy is a scalar quantity.
Pressure: Pressure is actually force acting on a body but in all directions and not in a particular direction.
In general we can define pressure by formula as below:
$P=\dfrac{F}{A}$
Where P = pressure
F = force
A = area
Though force is vector but direction is not specific and acts in all directions.
So pressure is also a scalar quantity.
Momentum: We can define momentum by a formula define below:
$p=m\times v$
Where p = momentum
m = mass
v = velocity
Now in this mass is scalar but velocity is a vector quantity.
For example if we throw a 5 kg ball In westward direction at 2 m/s.
In order to describe its momentum mass is 5 kg and velocity is 2 m/s.
Hence momentum (p) can be calculated as below
$\Rightarrow p=m\times v$
$\Rightarrow p=5kg\times 2m/s$
$\Rightarrow p=10kgm/\operatorname{s}$
We also need to specify direction of momentum.
Here direction will be the “ Direction in which the ball is thrown i.e. west”.
So momentum is a vector quantity.
Work: Work is defined as force which produces motion. It can be defined as a scalar or dot product of force and displacement. Dot product gives scalar quantity.
(If we have two vector quantity A and B having angle $\theta$ between them then there dot product can be defined as $A\centerdot B=AB\cos \theta$)
If force is F and displacement is d having angle between them is $\alpha$ then work can be defined as:
$\Rightarrow W=F\centerdot d$
$\Rightarrow W=Fd\cos \alpha$
Hence work is scalar in nature.
So out of options given the correct answer is option c i.e momentum.

Note: In vector quantity direction should be specific i.e in a particular direction only and not in all direction. We should keep it in mind while solving this question.