Question

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

Answer 1

Answer:

A.$1900 kg/m^3$

Explanation:

We are given that

$m=8.6 kg$

Density,$\rho_s=3400 kg/m^3$

Tension,T=38 N

We have to find the density of liquid.

$T=mg-\rho_l Vg$

$g=9.8 m/s^2$

Volume,V=$\frac{m}{\rho_s}$

$38=8.6\times 9.8-\rho_l\times \frac{8.6}{3400}\times 9.8$

$\rho_l\times \frac{8.6}{3400}\times 9.8=8.6\times 9.8-38$

$\rho_l=\frac{(8.6\times 9.8-38)\times 3400}{8.6\times 9.8}$

$\rho_l=1867kg/m^3\approx 1900 kg/m^3$

Option A is true.