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11 August, 09:19

A body weighs 10newton in air and 9.5 in water. How will it weigh in alchohol if density 0.8gcm-³

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  1. 11 August, 09:30
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    The weight of object in alcohol is, W₀ = 9.6 N

    Explanation:

    Given,

    The weight of body in air, Wₐ = 10 N

    The weight of the body in water, Wₓ = 9.5 N

    The density of the alcohol, ρ = 0.8 g/cm³

    = 800 kg/m³

    The weight of body in water = weight of object in air - weight of water displaced

    9.5 N = 10 N - weight of water displaced

    Weight of water displaced = 0.5 N

    The mass of the displaced water, m = 0.5 / 9.8

    = 0.051 kg

    Therefore the volume of the water displaced,

    V = m / ρ

    = 0.051 / 1000

    = 5.1 x 10⁻⁵ m³

    The volume of water displaced is equal to the volume of alcohol displaced

    Therefore, the mass of the alcohol displaced, = V x ρ

    = 5.1 x 10⁻⁵ x 800

    = 0.0405 kg

    The weight of the alcohol displaced, w = 0.0405 x 9.8

    = 0.4 N

    Therefore,

    The weight of body in alcohol = weight of object in air - weight of alcohol displaced

    W₀ = W - w

    = 10 N - 0.4 N

    = 9.6 N

    Hence, the weight of object in alcohol is, W₀ = 9.6 N
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