A sphere of mass of m = 1.40 kg is first placed directly on the plate of an elec

Question

A sphere of mass ofm= 1.40 kg is first placed directly on the plate of an electronic scale. The scale shows 13.73 N as the weight of the object. (See left figure.) A large beaker containing a liquid with a density of ?liquid= 725 kg/m3is 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 1.25 N with the sphere not touching the beaker. Calculate the density of the sphere. Can I have the answer and formulas in deatail. Assume that I dont know what any of the variables stand for. Thanks in advance.

Explanation / Answer

let the density of the sphere be k.so,

9.8*v*d=13.73

and v*9.8*d- 725*v*9.8= 1.25

solving we get d=797.616 kg/m^3

given

density =mass / volume

force balence= gravitational force=gvd=9.8*v*d=13.73 N-

=>v=13.73/9.8*d ---

--=> v*9.8*d - 725*v*9.8 = 1.25..

= (13.73/9.8d) [9.8d

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