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Two bodies of masses $m\: and \: 4m$ are placed at a distance $r$ . The gravitational potential at a point on the line joining them where the gravitational field is zero is

Option 1)
$zero$

Option 2)
$-\frac{4Gm}{r}$

Option 3)
$-\frac{6Gm}{r}$

Option 4)
$-\frac{9Gm}{r}$

Answers (1)

As we discussed in

Gravitational field due to Point mass -

$F=\frac{GmM}{r^{2}}$

$I= \frac{F}{m}= \frac{GMm}{r^{2}m}$

$\therefore I= \frac{GM}{r^{2}}$

$\dpi{100} G \rightarrow Gravitational\: constant$

$M\rightarrow mass\: of\: earth$

- wherein

As the distance (r) of test mass from point (M) Increases I decreases.

$I\propto \frac{1}{r^{2}}$

$I= 0\: at\: \left ( r= \infty \right )$

$\frac{Gm}{r^{2}}=\frac{G(4m)}{(r-x)^{2}}$

$\left [ \frac{x}{\left ( r-x \right )} \right ]^2=\frac{1}{4}$

$\Rightarrow x=\frac{r}{3}$

$U=\frac{-Gm}{x}-\frac{G\left ( 4m \right )}{\left ( r-x \right )}$

$=\frac{-Gm}{\left ( \frac{r}{3} \right )}-\frac{G\left ( 4m \right )}{\left ( r-\frac{r}{3} \right )}$

$= -\frac{3Gm}{r}-\frac{3G\left ( 4m \right )}{2r}$

$= -\frac{9Gm}{2r}$

Option 1)

$zero$

Incorrect option

Option 2)

$-\frac{4Gm}{r}$

Incorrect option

Option 3)

$-\frac{6Gm}{r}$

Incorrect option

Option 4)

$-\frac{9Gm}{r}$

Posted by

Sabhrant Ambastha

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