Infinite number of masses, each 2kg, are placed along the X− axis at x=±1m,±2m,±4m,±8m,±16m... The magnitude of the resultant gravitational potential in terms of gravitational constant G at the origin (x=0) is
A
−2G
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B
−4G
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C
−8G
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D
−16G
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Solution
The correct option is C−8G Gravitational potential at 0, V0=−(G×2)1(2)−(G×2)2(2)−(G×2)4×2...∞=−4G[11+12+14+....∞]=−4G⎡⎢
⎢
⎢
⎢⎣11−(12)⎤⎥
⎥
⎥
⎥⎦=−8G