Chapter 6, Problem 14A

The ratio of circumference/diameter for all circles is $\pi$. What is the ratio of force/mass for all freely-falling bodies?

To determine

Ratio of force to mass for all free falling body.

Answer to Problem 14A

Ratio of force to mass for all free falling body is $g$ .

Explanation of Solution

Given:

Ratio of circumference to diameter for all circles is $\pi$ .

Formula Used:

From Newton’s second law, the net force is given as

  $F=ma$

Where, $m$ is mass of object and $a$ is acceleration.

Calculation:

For a free falling body, the above relation modifies as

  $F_g=mg$

Where, $F_g$ force or weight of object, $m$ is mass of object and $g$ is acceleration due to gravity.

Now, ratio of force to mass is

  $\frac{F_g}{m}=g$

It is acceleration due to gravity.

Conclusion:

Therefore, the ratio of force to mass for all free falling body is $g$ .