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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

A
GMm(1+3)2L2
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B
GMmL2(1+3)
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C
GMm(13)2L2
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D
GMm(1+3)L2
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Solution

The correct option is A GMm(1+3)2L2
Net force on any mass at the position between two masses is zero

Let say the distance between M and m is "x" so the net force due to M and 3M on mass m is zero

so we have,

GMmx2=G3Mm(Lx)2

now by solving above equation

Lx=3x

x=L1+3

now by the formula of force between two mass

F=GMmx2

plug in the value of "x" in it

F=GMm(L1+3)2

F=GMm(3+1)2L2

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