Question

You are exploring a small moon of a distant planet. Measurements indicate that this moon is a sphere of uniform density rho = 5000 kg/m3. You dig a very deep hole into the moon that reaches within r0 = 1000 m of the center of the moon. With your spacesuit, you have a mass of m = 85 kg. Find the force of gravity on you when you stand at the bottom of the hole.

Answers

  1. Answer:

    The force of gravity will be “0.11874 N“

    Explanation:

    The given values are:

    Density of planet,

    Q = 5000 Kg/m³

    Inside radius,

    r₀ = 1000 m

    Now,

    The mass of inside sphere will be:

    ⇒  m_p=density\times volume

    ⇒        =5000\times \frac{4}{3}\pi r^3

    On putting the values, we get

    ⇒        =5000\times \frac{4}{3}\times \pi\times (1000)^3

    ⇒        =85 \ kg

    hence,

    The force of gravity will be:

    =  \frac{Gm_{planet} m_{person}}{r^2}  

    =  \frac{6.67\times 10^{-11}\times 5000\times 4\pi\times 85\times 1000}{3}

    =  \frac{6.67\times 10^{-11}\times 4\pi\times 425000000}{3}

    =  0.11874 \ N

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