Answer:
[tex]D = 0.42m[/tex]
Step-by-step explanation:
Given
Force = 0.052 N when Distance = 1.6 m
Required
Find Force; when distance = 0.74 N
The question says force is inversely proportional to square of distance;
Let F represent Force and D represent Distance;
Mathematically;
[tex]F\alpha \frac{1}{D^2}[/tex]
Convert proportion to equation
[tex]F = \frac{k}{D^2}[/tex]
Where k is the proportionality constant; This means that k is always constant
Make k the subject of formula
[tex]F * D^2 = \frac{k}{D^2} * D^2[/tex]
[tex]FD^2 = k[/tex]
When F = 0.052 and D = 1.6; the value of k is as follows
[tex]0.052 * 1.6^2 = k[/tex]
[tex]0.13312 = k[/tex]
[tex]k = 0.13312[/tex]
When F = 0.74;
Recall that k is always constant; so [tex]k = 0.13312[/tex]
To solve for D, we'll make use of [tex]F = \frac{k}{D^2}[/tex]
Substitute [tex]k = 0.13312[/tex] and F = 0.74;
[tex]0.74 = \frac{0.13312}{D^2}[/tex]
Multiply both sides by D²
[tex]0.74 * D^2 = \frac{0.13312}{D^2} *D^2[/tex]
[tex]0.74 * D^2 = 0.13312[/tex]
Divide both sides by 0.74
[tex]\frac{0.74 * D^2}{0.74} = \frac{0.13312}{0.74}[/tex]
[tex]D^2 = \frac{0.13312}{0.74}[/tex]
[tex]D^2 = 0.17989189189[/tex]
Take square roots of both sides
[tex]D = \sqrt{0.17989189189}[/tex]
[tex]D = 0.42413664294[/tex]
[tex]D = 0.42m[/tex] (Approximated)
