Question

Heya!!!!!!!⚫plz answer this question fastly⚫
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 gravitational force acting on it due masses M and 3M is zero. the magnitude of gravitational force acting due to mass M on mass m will be

Answer 1

First Of All We Know:  [F = $\frac{Gm1m2}{r^2}$]   [This is The Basic :P]

Let The Distance between M and m be 'a'

Because Net Force Is Zero...

$\frac{GMm}{a^2}$ - $\frac{G3Mm}{(L-a)^2}$ = 0

$\frac{GMm}{a^2}$ = $\frac{G3Mm}{(L-a)^2}$

On Solving, Above Equation.. The G, M, m will get Cancel and We Will Left Out With

L - a = √3a

L = a( 1 + √3 )

From Here a = $\frac{L}{(1+\sqrt{3})}$

Putting this in F = GMm/a²

F = $\frac{GMm}{ \frac{L}{(1+\sqrt{3})^{2}} }$

So F = $\frac{GMm(1 +\sqrt{3})^2} {L^2}$

Hope This Will Help You :)