A sphere of mass of m = 1.67 kg is first placed directly on the plate of an elec

Question

A sphere of mass of m = 1.67 kg is first placed directly on the plate of an electronic scale. The scale shows 16.38 N as the weight of the object. (See left figure.) A large beaker containing a liquid with a density of rho_liquid = 815 kg/m^3 is then placed on the scale and the scale is (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 2.61 N with the sphere not touching the beaker. Calculate the density of the sphere. A: 2.43 times 10^3 B: 3.53 times 10^3 C: 5.12 times 10^3 D: 7.42 times 10^3 E: 1.08 times 10^4 F: 1.56 times 10^4 G: 2.26 times 10^4 H: 3.28 times 10^4

Explanation / Answer

Weight gained on water scale = weight diplaced by ball

2.61 N = rhow*V*g=815*V*9.81

Volume of water replaced= volume of ball = V = 3.2644*10-4 m3

Density of the sphere = mass/ volume = M/V = 1.67/3.2644*10^-4 =5115.67 kg/m3

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