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Question

A large number of identical point masses m are placed along x-axis, at x=0,2,3,4,.........The magnitude of gravitational force on a mass m at origin (x=0), will be
x=0x=1x=2x=4 and so on
1209157_72ddeb43085746699e6665329d839c09.png

A
Gm2
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B
43Gm2
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C
23Gm2
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D
54Gm2
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Solution

The correct option is B 43Gm2
The gravitational force between any point is given by
F=Gm1m2r2

The gravitational force on mass m placed at x=0,
F=Gm2(1)2+Gm2(2)2+Gm2(3)2+Gm2(4)2+...........

F=Gm2(11+122+132+142+......)
F=Gm2(1112)
F=Gm243
F=4Gm23
The correct option is B.

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