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A solid sphere of mass 8.6 kg, made of metal whose density is 3,400 kg/, hangs by a cord. When the sphere is immersed in a liquid of unknown density, the tension in the cord is 38 N. The density of the liquid is closest to which one of the following values?A) 1900 kg/m³B) 1600 kg/m³C) 1700 kg/m³D) 1400 kg/m³E) 1500 kg/m³

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lublana

Answer:

A.[tex]1900 kg/m^3[/tex]

Explanation:

We are given that

[tex]m=8.6 kg[/tex]

Density,[tex]\rho_s=3400 kg/m^3[/tex]

Tension,T=38 N

We have to find the density of liquid.

[tex]T=mg-\rho_l Vg[/tex]

[tex]g=9.8 m/s^2[/tex]

Volume,V=[tex]\frac{m}{\rho_s}[/tex]

[tex]38=8.6\times 9.8-\rho_l\times \frac{8.6}{3400}\times 9.8[/tex]

[tex]\rho_l\times \frac{8.6}{3400}\times 9.8=8.6\times 9.8-38[/tex]

[tex]\rho_l=\frac{(8.6\times 9.8-38)\times 3400}{8.6\times 9.8}[/tex]

[tex]\rho_l=1867kg/m^3\approx 1900 kg/m^3[/tex]

Option A is true.

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