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The gravitational pull between two bodies is 20N. Find the gravitational pull when their distance of separation is doubled.

Physics

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Answer

D) 5N\text{D) 5N}

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Physics
The gravitational pull between two bodies is 20N. Find the gravitational pull when their distance of separation is doubled.

  1. Recall Newton's Law of Universal Gravitation.

    The gravitational force (FF) between two bodies is inversely proportional to the square of the distance (rr) between their centers.

    F∝1r2F \propto \frac{1}{r^2}

    This can be written as:

    F=Gm1m2r2F = G \frac{m_1 m_2}{r^2}

    where GG is the gravitational constant, and m1m_1 and m2m_2 are the masses of the two bodies.

  2. Set up the initial condition.

    Let the initial gravitational pull be F1=20 NF_1 = 20 \text{ N} at an initial distance r1r_1.
    So,

    F1=Gm1m2r12=20 NF_1 = G \frac{m_1 m_2}{r_1^2} = 20 \text{ N}
  3. Calculate the new gravitational pull when the distance is doubled.

    The new distance of separation is r2=2r1r_2 = 2r_1.
    Let the new gravitational pull be F2F_2.

    F2=Gm1m2r22F_2 = G \frac{m_1 m_2}{r_2^2}

    Substitute r2=2r1r_2 = 2r_1 into the equation:

    F2=Gm1m2(2r1)2F_2 = G \frac{m_1 m_2}{(2r_1)^2} F2=Gm1m24r12F_2 = G \frac{m_1 m_2}{4r_1^2} F2=14(Gm1m2r12)F_2 = \frac{1}{4} \left( G \frac{m_1 m_2}{r_1^2} \right)

    From Step 2, we know that Gm1m2r12=F1G \frac{m_1 m_2}{r_1^2} = F_1.
    So,

    F2=14F1F_2 = \frac{1}{4} F_1 F2=14(20 N)F_2 = \frac{1}{4} (20 \text{ N}) F2=5 NF_2 = 5 \text{ N}

    The final answer is D) 5N\text{D) 5N}.

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