Chapter 13, Problem 92A

To determine

To Show: The unit of force can be expressed in terms of $\text{kg/m}\cdot {\text{s}}^{\text{2}}$ .

Explanation of Solution

Introduction:

SI unit of pressure is Pascal. Pressure can also be expressed in terms of force per unit area.

Pressure can be expressed as,

  $P=\frac{F}{A}$  ...... (1)

Force can also be expressed as,

  $F=ma$  ...... (2)

Area can be expressed as,

  $A=L^2$

Here, $F,A,m$ and $a$ are the force, area, mass, and acceleration respectively.

Substitute $ma$ for $A$ in equation (1),

  $P=\frac{ma}{L^2}$  ....... (2)

Unit of mass is $\text{kg}$ .

Unit of acceleration is ${\text{ms}}^{\text{-2}}$

Unit of length is $m$

From equation (2), we have,

  $\begin{array}{l}P=\frac{\text{kg}\cdot \text{m}\cdot {\text{s}}^{\text{-2}}}{{\text{m}}^{\text{2}}}\\ P=\text{kg/m}\cdot {\text{s}}^{\text{2}}\end{array}$

Conclusion:

Hence, the unit of pressure i.e. Pascal can be expressed in terms of $\text{kg/m}\cdot {\text{s}}^{\text{2}}$ .