Chapter 7, Problem 59A

To determine

To prove: Unit of $g$ is ${\text{m/s}}^{\text{2}}$ as well as ${\text{N/m}}^{\text{2}}$ .

Explanation of Solution

Given:

Unit of g is $\text{N}/{\text{m}}^2$

Formula used:

The relation between force F, mass m and acceleration a is

  $F=ma$

Calculation:

Rearrange the force equation for acceleration.

  $a=\frac{F}{M}$

For the gravitational force,

  $g=\frac{F_r}{M}$

Unit of gravitational force is N and unit of mass is kg. So, unit of acceleration is $\text{N}/{\text{m}}^2$

Also, $1\text{N}=1{\text{kg-m/s}}^{\text{2}}$

So,

  $\begin{array}{c}\frac{\text{N}}{\text{kg}}=\frac{{\text{kg-m/s}}^{\text{2}}}{\text{kg}}\\ \text{=}{\text{m/s}}^{\text{2}}\end{array}$

Conclusion:

Hence , $\frac{\text{N}}{\text{kg}}={\text{m/s}}^{\text{2}}$