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 so that the net gravitational 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

Let the mass m be nearer to mass M, than mass 3M as the net force acting on it due to the two masses is 0.As 3M>M,so the point mass m mustn't not be experiencing much force of attraction of 3M.Let the distance between m and M be x.So distance between 3M and m is (l-x ) m.(as total distance between them is l.l.)

Force of attraction between m and M :

F= GMmx2...(i)GMmx2...(i)

Force of attraction between 3M and m :

3GMm(l−x)2...(ii)3GMm(l−x)2...(ii)

Eqns (i) and (ii) are equal,as the net force is zero.So,

GMmx2=3GMm(l−x)2GMmx2=3GMm(l−x)2

i.e, (l−x)2=3x2(l−x)2=3x2

(l−x)=3–√xl−x)=3x (Taking square root )

or

l=3–√x+xl=3x+x

Or

x=l3–√+1l3+1

As x is distance between m and M, you can find the force of attraction between m and M.You will find the answer corresponds to (a)