Question

The force,

F
(Newtons), between two objects is inversely proportional to the square of the distance,
d
(metres), between them.
The force is 0.009 Newtons when the distance between the objects is 2 metres.
Work out
d
(rounded to 2 DP) when
F
=
0.062
Newtons.

Answer 1

`\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] \rule{34em}{0.25pt}`

`\begin{array}{llll} \textit{`

`0.009=\cfrac{k}{(2)^2}\implies 0.009=\cfrac{k}{4}\implies 0.036=k~\hfill \boxed{F=\cfrac{0.036}{d^2}} \\\\\\ \textit{when F = 0.062, what is`