ExamBro
ExamBro
AP EAMCET · PHYSICS · Gravitation

An infinite number of objects each 1 kg mass are placed on the x -axis on both sides of \(\mathrm{x}=0\) at \(\pm 1 \mathrm{~m}, \pm 2 \mathrm{~m}, \pm 4 \mathrm{~m}, \pm 8 \mathrm{~m} \ldots\) and so on. The magnitude of the resultant gravitational potential (in SI units) at \(x=0\) is
(G - Universal gravitational constant)

  1. A \(-G\)
  2. B \(-2 \mathrm{G}\)
  3. C \(-3 \mathrm{G}\)
  4. D \(-4 \mathrm{G}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(-4 \mathrm{G}\)

Step-by-step Solution

Detailed explanation

\(V = \sum_{n=0}^{\infty} \left( -\frac{Gm}{2^n} \right) + \sum_{n=0}^{\infty} \left( -\frac{Gm}{2^n} \right)\) \(V = -2Gm \sum_{n=0}^{\infty} \left(\frac{1}{2}\right)^n\) \(V = -2G(1) \left(\frac{1}{1 - \frac{1}{2}}\right)\) \(V = -2G(2)\) \(V = -4G\)
Same subject
Explore more questions on app
From AP EAMCET
Explore more questions on app