Question

Two point masses $M$ and $3M$ are placed at a distance $L$ apart. Another point mass $m$ is placed in between on the line joining them so that the net gravitioanl force acting on it due to masses $M$ and $3M$ is zero. The magnitude of gravitational force acting due to mass $M$ on mass $m$ will be

Answer 1

According to question we can say that $F_{mM}=F_{m3M}$

$\frac{GmM}{r^2}=\frac{Gm3M}{(l-r{)}^2}$ here r= distance of mass m from M

after canceling the terms and cross multiplying , we get $(l-r{)}^2=3r^2$

it gives $l-r=\sqrt{3}r$

we get , $r=\frac{l}{1+\sqrt{3}}$

Now , force on m due to M $F_{mM}=\frac{GmM}{l^2}(1+\sqrt{3}{)}^2$