A cylindrically shaped container, open at the top, rests on a scale. Its height

Question

A cylindrically shaped container, open at the top, rests on a scale. Its height is 0.100 m and its weight can be neglected. When it is filled to the top with a fluid whose density is p = 890 kg/m' , the scale reads 1.00 N . (Figure 1) A sphere of density P_b = 5000kg/m^3 and volume V = 60.0 cm^3 is then submerged in the fluid, so that some fluid spills over the container's side. The sphere is held in place by a stiff rod whose volume and weight can be neglected. In this problem, use g = 9.81 m/s^2 for the acceleration due to gravity. Determine the weight W_3 now shown on the scale. Express your answer numerically in newtons.

Explanation / Answer

volume of sphere = 60 cm^3

so same amount of water will be displaced by the sphere

60 cm^3 = 6 * 10^-5 m^3

mass of 6 * 10^-5 m^3 of liquid

density = mass / volume

890 = mass / (6 * 10^-5)

mass = 0.0534 kg

weight = mass * g

weight of water displaced = 0.0534 * 9.81

weight of remaining water = 1 - 0.0534 * 9.81

weight of remaining water = 0.476146 N

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