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Gravitation

Section: Physics

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Question : 8 of 18

Marks: +1, -0

An infinite number of objects each 1 kg mass are placed on the

x

-axis on both sides of

x=0

\pm 1 \mathrm{m}, \pm 2 \mathrm{m}, \pm 4 \mathrm{m}, \pm 8 \mathrm{m}

... and so on. The magnitude of the resultant gravitational potential (in SI units) at

x=0

(G - Universal gravitational constant)

[AP EAPCET 21 May 2025 S1]

$-G$
$-2G$
$-3G$
$-4G$

Solution:

Gravitational potential

V=-\frac{G m}{r}

Since, the mass of each object is 1 kg and the distance are

1,2,4,8,\dots

on both sides of

x=0

. Thus, the total potential at

x=0

V_{\text{total}}=-G\left(\frac{m_1}{r_1}+\frac{m_2}{r_2}+\frac{m_3}{r_3}+\dots\right)

-G\left(\frac{m_1}{r_1}+\frac{m_2}{r_2}+\frac{m_3}{r_3}+\dots\right)

=-2G\left(\frac{1}{1}+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\dots\right)

=-2G\left(\frac{1}{1-\frac{1}{2}}\right)=-4G

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