Physics

Question

A 2.0-kilogram mass is located 3.0 meters above
the surface of Earth. What is the magnitude of
Earth’s gravitational field strength at this
location?
(1) 4.9 N/kg (3) 9.8 N/kg
(2) 2.0 N/kg (4) 20. N/kg

2 Answer

  • (3) 9.8 N/kg is your answer.
  • The correct answer is: Option (3) 9.8 N/kg

    Explanation:

    According to Newton's Law of Gravitation:

    [tex] F_g = \frac{GmM}{R^2} [/tex] --- (1)

    Where G = Gravitational constant = 6.67408 × 10⁻¹¹ m³ kg⁻¹ s⁻²

    m = Mass of the body = 2 kg

    M = Mass of the Earth = 5.972 × 10²⁴ kg

    R = Distance of the object from the center of the Earth = Radius of the Earth + Object's distance from the surface of the Earth = (6371 * 10³) + 3.0 = 6371003 m

    Plug in the values in (1):

    (1)=> [tex] F_g = \frac{6.67408 * 10^{-11} * 2 * 5.972*10^{24}}{(6371003)^2} = 19.63 [/tex]

    Now that we have force strength at the location, we can use:

    Force = mass * gravitational-field-strength

    Plug in the values:

    19.63 = 2.0 * gravitational-field-strength

    gravitational-field-strength = 19.63/2 = 9.82 N/kg

    Hence the correct answer is Option (3) 9.8 N/kg

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