In the above problem, the ratio of the time duration of his jump on the moon to that of his jump on the earth 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
    <p>6. In the above problem, the ratio of the time duration of his jump on the moon to that of his jump on the earth is:</p>

    Question:

    6. In the above problem, the ratio of the time duration of his jump on the moon to that of his jump on the earth is:

    • a) 1 : 6
    • b) 6 : 1
    • c) √6 : 1
    • d) 1 : √6

    Answer:

    6. (b)

    ge / gm = (Re ρe) / (Rm ρm) = (2 / 3) × (4 / 1) = 6 or gm = ge / 6

    For motion on earth, using the relation,

    s = ut + (1 / 2) at2

    We have, (1 / 2) = 0 + (1 / 2) × 9.8r2 or t = 1 / √9.8 s

    For motion on the moon, 3 = 0 + (1 / 2) (9.8 / 6) t12

    or t1 = 6√9.8 s ∴ t1 / t = 6 or t1 = 6t

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