If F - GmM - r 2- then dF - dr -A- -2 GmM - r 3- 2 Gm M - r 3- 0D- 1

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Principle of Superposition

If F = GmM / ...

Question

If $F = \frac{G m M}{r^{2}}$ , then $\frac{d F}{d r} = ?$

- \frac{2 G m M}{r^{3}}

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\frac{2 G m M}{r^{3}}

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Solution

The correct option is A $- \frac{2 G m M}{r^{3}}$
$F = \frac{G M m}{r^{2}}$
By rearranging, we have
$F = G M m r^{- 2}$
By differentiating w.r.t. $r$ , we have
$\frac{d F}{d r} = G M m (- 2) r^{- 3}$
$= - 2 \frac{G M m}{r^{3}}$

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If F=GmMr2, then dFdr=?

The correct option is A −2GmMr3F=GMmr2 By rearranging, we have F=GMmr−2 By differentiating w.r.t. r , we have dFdr=GMm(−2)r−3 =−2GMmr3

If $F = \frac{G m M}{r^{2}}$ , then $\frac{d F}{d r} = ?$

The correct option is A $- \frac{2 G m M}{r^{3}}$
$F = \frac{G M m}{r^{2}}$
By rearranging, we have
$F = G M m r^{- 2}$
By differentiating w.r.t. $r$ , we have
$\frac{d F}{d r} = G M m (- 2) r^{- 3}$
$= - 2 \frac{G M m}{r^{3}}$