A sphere of mass of m = 1.11 kg is first placed directly on the plate of an elec
ID: 1262634 • Letter: A
Question
A sphere of mass of m = 1.11 kg is first placed directly on the plate of an electronic scale. The scale shows 10.89 N as the weight of the object. (See left figure.) A large beaker containing a liquid with a density of ?liquid = 651 kg/m3 is then placed on the scale and the scale is tared (i.e. zeroed to this weight as a reference point, it has a reading of zero with the beaker on the scale). The sphere, hung by a thin string, is lowered into the liquid and submerges below the surface. (See right figure.) The scale reads 1.51 N with the sphere not touching the beaker. Calculate the density of the sphere.
A sphere of mass of m = 1.11 kg is first placed directly on the plate of an electronic scale. The scale shows 10.89 N as the weight of the object. (See left figure.) A large beaker containing a liquid with a density of ?liquid = 651 kg/m3 is then placed on the scale and the scale is tared (i.e. zeroed to this weight as a reference point, it has a reading of zero with the beaker on the scale). The sphere, hung by a thin string, is lowered into the liquid and submerges below the surface. (See right figure.) The scale reads 1.51 N with the sphere not touching the beaker. Calculate the density of the sphere.Explanation / Answer
The buoyant force on the sphere is 10.89 N - 1.51 N = 9.38 N
This buoyant force is related to the mass of the water displaced by 9.38 N / 9.8m/s^2 = 0.96 kg water displaced.
The volume of this water and thus the volume of the sphere is
0.96 kg / 651 kg/m^3 = 1.475 x 10^-3 m^3
The sphere's density is its mass / that volume = 1.11 kg / (1.475 x 10^-3)m^3 = 752.72 kg/m^3
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