Let “g” be the acceleration due to gravity at Earth’s surface, and “K” be the Earth’s rotational kinetic energy. If Earth’s radius decreases by 2%, keeping all other factors the same, what happens?

Posted on by Bookflicker0 Posted in Questions
    <p>3. Let g be the acceleration due to gravity at earth’s surface and K be the rotational kinetic energy of the earth. Suppose the earth’s radius decreases by 2% keeping all other quantities the same, then:</p>

    Question:

    3. Let g be the acceleration due to gravity at earth’s surface and K be the rotational kinetic energy of the earth. Suppose the earth’s radius decreases by 2% keeping all other quantities the same, then:

    • a) g decreases by 2% and K decreases by 4%
    • b) g decreases by 4% and K increases by 2%
    • c) g increases by 4% and K increases by 4%
    • d) g decreases by 4% and K increases by 4%

    Answer:

    3. (c) g = GM / R2 and K = L2 / 2I

    If mass of the earth and its angular momentum remains constant, then:

    g ∝ 1 / R2 and K ∝ 1 / R2

    i.e., if the radius of earth decreases by 2%, then g and K both increase by 4%

    Verified by Bookflicker Expert