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 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 (1)  2 2 GMm 1 3 L  (2)   2 3 1 3 GMm L  (3)   2 2 GMm 1– 3 L (4)  

Answer 1

hey mate

here is your answer

Answer 2

Answer: $G \frac{Mm(1+\sqrt3)^2}{L^2}$

Explanation:

Let the mass m be located at a distance x from mass M. Therefore, the distance between m and 3M is L-x.

The magnitude of gravitational force between two masses is

$F=G\frac{M_1 M_2}{R^2}$

The gravitational force between mass M and m is:

$F_1=G\frac{Mm}{x^2}$

The gravitational force between 3M and m is

$F_2=G\frac{3Mm}{(L-x)^2}$

The net force on mass m is zero due to mass M and 3M

$\Rightarrow F_1=F_2\\ \Rightarrow G\frac{Mm}{x^2}=G\frac{3Mm}{(L-x)^2}\\ \Rightarrow (L-x)^2=3x^2\\ \Rightarrow x=\frac{L}{1+\sqrt 3}$

Ignoring the negative value.

The magnitude of gravitational force acting due to mass M on m will be:

$F_1=G\frac{Mm}{x^2}=G\frac{Mm (1+\sqrt 3)^2}{L^2}$