Physics Question?

An object takes 2.55 s to fall 5.35 m on a certain planet. Find the planet's mass if its radius is 5250 km.

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  • Anonymous
    1 month ago
    Favorite Answer

    2h = g*t^2

    g = 2h/t^2 = 10.7/2.55^2 = 1.646 m/sec^2 = M*G/r^2 (G = 6.674*10^-11)

    M = g*r^2/G = 1.646*5.25^2*10^12*10^11/6.674 = 6.80*10^23 kg

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  • MyRank
    Lv 6
    1 month ago

    Given,

    Time (t) = 2.55 sec

    Height (h) = 5.35 m

    Mass (m) = ?

    Radius (r) = 5250 km = 5250 x 10³m

    We know that:-  

    Acceleration due to gravity (g) = Gm/r²

    Mass (m) = gr²/G = 2hr²/t²G [∵ h = ½gt²]

    2 x 5.35 x (5250 x 10³)² / (2.55)² x 6.67 x 10⁻¹¹

    = 294918750 x 10⁶ / 43.37 x 10⁻¹¹≈ 6.80 x 10²³kg

    ∴ Mass (m) = 6.80 x 10²³kg.

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  • 1 month ago

    d = distance of fall = 5.35 m

    t = time of fall = 2.55 s

    a = gravitational acceleration = to be determined

    d = 0.5at²

    2d = at²

    2d/t² = a

    a = 2d/t²

    a = (2 x 5.35 m) / (2.55 s)²

    a = 1.645520953 m/s² ≈ 1.65 m/s²

    G = universal gravitational constant = 6.67E-11 N·m²/kg²

    r = radius = 5,250 km = 5,250,000 m

    m = mass = to be determined

    m = ar²/G

    m = (1.65 m/s²)(5.25E+06 m)²/(6.67E-11 N·m²/kg²)

    m = 6.80E+23 kg ANSWER

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  • 1 month ago

    h = ½gt²

    5.35 = ½g(2.55)²

    g = 2•5.35/(2.55)² = 1.646 m/s²

    g = GM/r² = 1.646

    M = (1.646)(5250000)² / 6.674e-11 = 6.80e23 kg or 6.80x10²³

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  • Dylan
    Lv 6
    1 month ago

    s = 0.5*at^2 + vt

    5.35 = 0.5*g*2.55^2

    g = 1.6455 m/s^2

    g = GM/r^2

    M = gr^2/G

     = 1.6455*5,250,000^2/(6.67408*10^-11)

     = 6.80*10^23 kg

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