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14 June, 09:21

A rock has mass 1.80 kg. When the rock is suspended from the lower end of a string and totally immersed in water, the tension in the string is 12.8 N. What is the smallest density of a liquid in which the rock will float?

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  1. 14 June, 10:32
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    3644.63 kg/m^3

    Explanation:

    mass of rock, m = 1.80 kg

    Weight of rock in water = 12.8 N

    Weight of rock in water = Weight of rock in air - Buoyant force on the rock due to water

    Buoyant force in water = 1.8 x 9.8 - 12.8 = 17.64 - 12.8 = 4.84 N

    Volume x density of water x g = 4.84

    V x 1000 x 9.8 = 4.84

    V = 4.939 x 10^-4 m^3

    For the rock to float in a liquid

    Buoyant force due to liquid on rock = weight of the rock

    V x density of liquid x g = 1.80 x g

    density of liquid = 1.80 / (4.939 x 10^-4) = 3644.63 kg/m^3
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