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Gravitation question

2013 · Q151
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Gravitation question

2013 · Q151

NEETPhysicsGravitationMCQ+4 / −1
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
  1. A
    −43- {4 \over 3}−34​ G
  2. B
    −-− 4G
  3. C
    −-− G
  4. D
    −83- {8 \over 3}−38​ G
View written solutionFree

Correct answer: B

Gravitational potential V = −Gmr{{ - Gm} \over r}r−Gm​

V0=−G×21−G×22−G×24−G×28{V_0} = - {{G \times 2} \over 1} - {{G \times 2} \over 2} - {{G \times 2} \over 4} - {{G \times 2} \over 8}V0​=−1G×2​−2G×2​−4G×2​−8G×2​

= −2G[1+12+14+18+...∞] - 2G\left[ {1 + {1 \over 2} + {1 \over 4} + {1 \over 8} + ...\infty } \right]−2G[1+21​+41​+81​+...∞]

=−2G×11−12 = - 2G \times {1 \over {1 - {1 \over 2}}}=−2G×1−21​1​

=−2G×112=−4G = - 2G \times {1 \over {{1 \over 2}}} = - 4G=−2G×21​1​=−4G

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