A solid sphere of mass 8.6 kg,made of metal whose density is 3400 kg/ $m ^ { 3 }$ ,hangs by a cord.When the sphere is immersed in a liquid of unknown density,the tension force that the cord exerts on the sphere is 38 N.The density of the liquid is closest to which one of the following values?
A)1900 kg/ $m ^ { 3 }$
B)1700 kg/ $m ^ { 3 }$
C)1600 kg/ $m ^ { 3 }$
D)1500 kg/ $m ^ { 3 }$
E)1400 kg/ $m ^ { 3 }$

Question

Quizplus · Accepted Answer

The tension in the cord when the sphere is immersed in the liquid is less than the weight of the sphere due to the buoyant force. The buoyant force equals the weight of the displaced liquid. First, find the volume of the sphere using its mass and the density of the metal: $V = \frac{m}{\rho_{metal}} = \frac{8.6}{3400}$ m$^3$. The weight of the sphere is $W = mg = 8.6 \times 9.8$ N. The tension force is 38 N, so the buoyant force is $W - T = 8.6 \times 9.8 - 38$ N. The weight of the displaced liquid equals the buoyant force, so $W_{liquid} = \rho_{liquid} V g$. Solving for $\rho_{liquid}$ gives a value closest to 1900 kg/m$^3$.

A Solid Sphere of Mass 8 m3m ^ { 3 }m3

A Solid Sphere of Mass 8 $m ^ { 3 }$