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Gravitation question

2023 · 1 Feb · Shift 1 · Q55
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Gravitation question

2023 · 1 Feb · Shift 1 · Q55

JEE MainPhysicsGravitationMCQ+4 / −1
Given below are two statements: Statement I: Acceleration due to gravity is different at different places on the surface of earth. Statement II: Acceleration due to gravity increases as we go down below the earth's surface. In the light of the above statements, choose the correct answer from the options given below
  1. A
    Both Statement I and Statement II are true
  2. B
    Both Statement I and Statement II are false
  3. C
    Statement I is false but Statement II is true
  4. D
    Statement I is true but Statement II is false
View written solutionFree

Correct answer: D

  1. Analyze Statement I

    Statement I says: Acceleration due to gravity is different at different places on the surface of earth.

    This is true.

    Reason:

    • The Earth is not a perfect sphere; it is slightly flattened at the poles.
    • Also, due to Earth's rotation, the effective acceleration due to gravity changes with latitude.
    • Hence, ggg is maximum near the poles and minimum near the equator.

    Therefore, Statement I is true.

  2. Analyze Statement II

    Statement II says: Acceleration due to gravity increases as we go down below the earth's surface.

    This is false.

    Reason:

    • Inside the Earth, only the mass enclosed within radius rrr contributes to gravity at that point.
    • As we go below the surface, the effective radius decreases, and the enclosed mass effect makes ggg decrease.
    • For a depth ddd below the surface, gd=g(1−dR)g_d = g\left(1 - \frac{d}{R}\right)gd​=g(1−Rd​) where RRR is the radius of Earth.
    • So, as ddd increases, gdg_dgd​ decreases.

    Therefore, Statement II is false.

  3. Choose the correct option

    • Statement I: True
    • Statement II: False

    Hence, the correct option is: D: Statement I is true but Statement II is false\boxed{\text{D: Statement I is true but Statement II is false}}D: Statement I is true but Statement II is false​

  4. Comparison with stored correct answer

    Stored correct answer: D

    My derived answer is also D, so they match.

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