Question

(1) SI unit of pressure is- A. $N{m^2}$ B. $Nm$ C. $N/{m^2}$ D. $N/m$
(2) Dimension of pressure is A. $\left[ {{L^1}{M^1}{T^{ - 2}}} \right]$ B. $\left[ {{L^1}{M^1}{T^{ - 1}}} \right]$ C. $\left[ {{L^1}{M^1}{T^2}} \right]$ D. $\left[ {{L^1}{M^1}{T^1}} \right]$
(3) Pressure is a _______ quantity.
A. Unitless
B. Scalar
C. Vector
D. None

Answer 1

Hint From the definition of pressure we can determine its unit, dimension and also tell if it’s a scalar or a vector quantity.
Formula used
$p = \dfrac{F}{A}$
Where $p$is the pressure, $F$ is the perpendicular force exerted on the surface area $A$ of an object.

Complete step by step answer
Pressure is defined as the force applied per unit area on an object. The force applied is perpendicular to the surface area of the object. The symbol for it is $p$.
Mathematically, the formula for pressure can be written as
$p = \dfrac{F}{A}$
Where $p$ is the pressure, $F$is the perpendicular force exerted on the surface area $A$ of an object.
The SI unit of pressure is Pascal which is usually represented as $Pa$ or Newton per square metre $N/{m^2}$ where $N$ the SI unit of force and ${m^2}$is the SI unit of area.

So, the correct option for the first question is C.

Pressure can also be expressed in other units such as $dyn/c{m^2}$, $atm$ and $J/{m^3}$.
Dimension of a physical quantity is represented by expressing the quantity in terms of the fundamental units length, mass and time.
The SI unit of pressure is force per unit area. So to determine its dimension, we first need to determine the dimensions of force and area.
$F = $ mass* acceleration.
$F = ML{T^{ - 2}}$and $A = {L^2}$
So, we have
$\begin{gathered}
  p = \dfrac{{ML{T^{ - 2}}}}{{{L^2}}} \\
   \Rightarrow p = {M^1}{L^{ - 1}}{T^{ - 2}} \\
\end{gathered} $
Scalar quantity defines a physical quantity which has no direction and only magnitude. Pressure is a physical quantity which has no particular direction but it has a definite value. For example, gas molecules exert pressure in every possible direction in random. We can change the vessel containing the gas, shrink it or expand it, pressure will still have a single value at that point.

Therefore, the correct option for the third question is B.

Note Air pressure is generated due to the constant random motion of the molecules which constantly collide with the walls of the container or other bodies in contact. We can measure air pressure using a device called the barometer.