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)2L2Net force on any mass at the position between two masses is zeroLet say the distance between M and m is "x" so the net force due to M and 3M on mass m is zeroso we have,GMmx2=G3Mm(L−x)2now by solving above equationL−x=√3x→x=L1+√3now by the formula of force between two massF=GMmx2plug in the value of "x" in itF=GMm(L1+√3)2F=GMm(√3+1)2L2

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