Question

State whether ‘Momentum’ is a scalar or vector?

Answer 1

Hint – We will start this question by defining all the terms, i.e., scalar quantity, vector quantity and momentum. We will use the formula of momentum, i.e., Momentum = Mass $ \times $ Velocity, we will also define mass and velocity to get the required answer.

Complete step-by-step solution -
We know that,
The physical quantities which have only magnitude and no direction are called scalar quantities or scalars. A scalar quantity can be specified by a single number, along with proper units.
Also,
The physical quantities which have both magnitude and direction and obey the laws of vector addition are called vector quantities or vectors. A vector quantity is specified by a number with a unit and its direction.
We know that,
Momentum of a body (or moving body) is defined as the product of mass of that body and velocity of that body. It is denoted by $p$.
The formula for calculating the momentum of a body is,
$p = mv$
where $m$ represents the mass and $v$ represents the velocity of the object.
Mass is a measure of the amount of matter of a body with no definite shape. As mass has only magnitude therefore it is a scalar quantity.
Velocity is the rate of change of position of an object with time in a given direction. It can also be defined as the speed of an object in a given direction. It is equal to the displacement covered per unit time. As velocity has both magnitude and direction, it is a vector quantity.
We know that the dot product of a scalar quantity and a vector quantity is again a vector quantity.
As momentum is also a dot product of a scalar quantity, i.e., mass and a vector quantity, i.e., velocity which is again a vector quantity.
Therefore, Momentum is a vector quantity.

Note - Momentum of a body (or moving body) is defined as the product of mass of that body and velocity of that body. It is denoted by $p$. The formula for calculating the momentum of a body is $p = mv$. We can solve this question if we know all about the scalar and vector quantities and all the definitions and formulas.