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Gravitational Potential & Energy question from NEET 2013

Q31NEET 2013Medium

Gravitational Potential & Energy

Infinite number of bodies, each of mass 2 kg are situated on x-axis at distance 1 m, 2 m, 4 m, 8 m,..., respectively, from the origin. The resulting gravitational potential due to this system at the origin will be

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Answer: (b)

$V = -G\cdot 2\left(\frac{1}{1} + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \dots\right)$
Infinite GP sum: $\frac{1}{1-\frac{1}{2}} = 2$
$V = -2G \times 2 = -4G$
So the answer is (b) $-4G$ .

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