A solid sphere of uniform density has a mass of 3.0 × 104 kg and a radius of 1.0 m. What is the magnitude of the gravitational force due to

Question

A solid sphere of uniform density has a mass of 3.0 × 104 kg and a radius of 1.0 m. What is the magnitude of the gravitational force due to the sphere on a particle of mass 9.3 kg located at a distance of (a) 1.4 m and (b) 0.21 m from the center of the sphere? (c) Write a general expression for the magnitude of the gravitational force on the particle at a distance r ≤ 1.0 m from the center of the sphere.

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Acacia 4 years 2021-07-20T12:58:41+00:00 1 Answers 30 views 0

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  1. taiduc
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    2021-07-20T13:00:27+00:00
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    Answer:

    a) Fg = 9.495×10⁻⁶N

    b) Fg = 3.908×10⁻⁶N

    c)

    F_{g} =\frac{Gm_{1}m_{2}R }{r^{3} }

    Explanation:

    Given:

    m₁ = mass = 3×10⁴kg

    r = radius = 1 m

    m₂ = 9.3 kg

    Questions:

    a) What is the magnitude of the gravitational force due to the sphere located at R = 1.4 m, Fg = ?

    b) What is the magnitude of the gravitational force due to the sphere located at R= 0.21 m, Fg = ?

    c) Write a general expression for the magnitude of the gravitational force on the particle at a distance r ≤ 1.0 m from the center of the sphere.

    a) Since R > r, the equation for the gravitational force is:

    F_{g} =\frac{Gm_{1}m_{2} }{R^{2} }

    Here,

    G = gravitational constant = 6.67×10⁻¹¹m³/s² kg

    Substituting values:

    F_{g} =\frac{6.67x10^{-11}*3x10^{4}*9.3 }{1.4^{2} } =9.495x10^{-6} N

    b) Since R < r, the equation for the gravitational force is:

    F_{g} =\frac{Gm_{1}m_{2}R }{r^{3} } =\frac{6.67x10^{-11}*3x10^{4}*9.3*0.21 }{1^{3} } =3.908x10^{-6} N

    c) The general expression for the magnitude of the gravitational force on the particle at a distance r ≤ 1.0 is the same to b)

    F_{g} =\frac{Gm_{1}m_{2} R}{r^{3} }

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