Answer
(a) $\frac{dF}{dr}$ = $-2\frac{GmM}{r^{3}}$
the minus mean the distance increases, the force decreases
(b) $16$ $N/km$
Work Step by Step
(a)
$\frac{dF}{dr}$ = $-2\frac{GmM}{r^{3}}$
the minus mean the distance increases, the force decreases
(b)
$F'(r)$ = $-2\frac{GmM}{r^{3}}$
$F'(20,000)$ = $-2\frac{GmM}{(20000)^{3}}$
$2$ = $-2\frac{GmM}{(20000)^{3}}$
$GmM$ = $-(20000)^{3}$
$F'(10,000)$ = $-2\frac{-(20000)^{3}}{(10000)^{3}}$
$F'(10,000)$ = $16$ $N/km$