A sphere of mass of m = 1.72 kg is first placed directly on the plate of an elec

Question

A sphere of mass of m = 1.72 kg is first placed directly on the plate of an electronic scale. The scale shows 16.87 N as the weight of the object. (See left figure.) A large beaker containing a liquid with a density of liquid = 887 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 2.73 N with the sphere not touching the beaker. Calculate the density of the sphere.

https://s4.lite.msu.edu/enc/56/58e1c3761f32f39ce705f0cbb3ade992b8ecbd735c9907a659036da0b4b7b0a6fd96344f36cbea9cf054437bdad70d40651ea7ee5c7da55cfbf0a48ee9330e07475569243a550b56.gif

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Explanation / Answer

The buoyant force on the sphere is 16.87 N - 2.73 N = 14.14 N

This buoyant force is related to the mass of the water displaced by 14.14N

mass of water displaced = 14.14N / 9.8m/s2 = 1.44 kg water

The volume of this water and thus the volume of the sphere is
1.44 kg / 877kg/m^3 = 1.625 x 10-3 m3

The sphere's density = mass / that volume

= 1.72kg / (1.625x10-3)m3
= 1058.45 kg/m3

According to the option given , option B. 9.90x102 is correct

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