Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

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

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main Maths 2025: Five tips to score high marks in ‘toughest’ subject; most important chapters

anam-khan

JEE Main 2025 exam city intimation slip for session 1 soon at jeemain.nta.nic.in

anam-khan

Focus on modern physics, formulas to solve tricky problems; 5 tips to tackle JEE Main physics 2025

Latest Question