Question

Which of the following is not a vector?
a) Linear momentum
b) Electric field intensity
c) Kinetic energy
d) Acceleration

Answer 1

Hint: Check out if any of them can be described by direction. Write down the formulas and check each and every term if they describe direction or just magnitude. A scalar will only have magnitude whereas a vector will have both magnitude and direction.

Formula used:
$\begin{align}
  & p=mv \\
 & E=\dfrac{F}{q} \\
 & K.E=\dfrac{1}{2}m{{v}^{2}} \\
 & a=\dfrac{v}{t} \\
\end{align}$

Complete answer:
Linear momentum is defined as the product of an object’s mass and its velocity. If we check each and every term in it, mass is a scalar and velocity is a vector quantity. Velocity describes both magnitude and direction. If we assume the mass m, velocity as v and momentum as p,

 $p=m \times v$

Electric field intensity is the electric force exerted or experienced by a unit positive charge at a certain position. As we know, electric force is a vector quantity and charge is a scalar quantity, it is termed as vector quantity. F be the force and q be the unit charge and electric field intensity E,

$E=\dfrac{F}{q}$

Kinetic energy is the energy possessed by any object due to its motion. It is the product of mass and square of velocity. Mass is scalar and velocity is vector, but the dot product of two vectors is a scalar quantity, thus, kinetic energy is a scalar quantity. Let m be the mass and v is the velocity, K.E is

$K.E=\dfrac{1}{2}m{{v}^{2}}$

Acceleration is the rate of change of velocity per unit time. It is only defined when velocity of the object changes, so, as velocity is vector quantity, acceleration is also a vector quantity.
$a=\dfrac{v}{t}$

So, the correct answer is “Option C”.

Note:
Dot product of two vectors is a scalar quantity whereas the cross product of two vectors is a vector quantity itself. Sometimes, dot products can also be called a scalar product and the cross product can be called a vector product.