A sphere of mass of m = 1.46 kg is first placed directly on the plate of an elec

Question

A sphere of mass of m = 1.46 kg is first placed directly on the plate of an electronic scale. The scale shows 14.32 N as the weight of the object. (See left figure.) A large beaker containing a liquid with a density of liquid = 643 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 2.69 N with the sphere not touching the beaker. Calculate the density of the sphere.

Explanation / Answer

We know that the buoyant force is equal to weight of the liquid displaced

W = volume x density x g

V * 643 * 9.8 = 2.6

V = 4.12 10 -4 m3

Hence the density of the sphere will be

Density = Mass / Volume

Volume of displaced liquid is equal to the volume of sphere.

Density = 1.46/4.12 10 -4 = 3543 kg/m3

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