Infinite number of masses, each 1 kg, 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:

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    <p>5. Infinite number of masses, each 1 kg, 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:</p>

    Question:

    5. Infinite number of masses, each 1 kg, 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) G/2
    • b) G
    • c) 2G
    • d) 4G

    Answer:

    5. (c) Gravitational potential:

    V = GM(1 / r1 + 1 / r2 + 1 / r3 + …)

    V = G × 1(1 / 1 + 1 / 2 + 1 / 4 + 1 / 8 + 1 / 16 + …)

    V = G(1 / (1 – 1 / 2)) (∴ sum of GP = a / (1 – r))

    V = 2G

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