A 6.1-kg solid sphere, made of metal whose density is 2600 kg/m³, is suspended by a cord. When the sphere is immersed in a liquid of unknown density, the tension in the cord is 26 N. Find the density of the liquid. A) 1500 kg/m³ B) 1400 kg/m³ C) 1300 kg/m³ D) 1200 kg/m³ E) 1100 kg/m³

Question

Quizplus · Accepted Answer

When the sphere is immersed in the liquid, the buoyant force acting on it is equal to the weight of the liquid displaced by the sphere. The tension in the cord is equal to the weight of the sphere minus the buoyant force. Therefore, the density of the liquid can be calculated as follows:$$density_{liquid} = \frac{weight_{sphere} - tension}{volume_{sphere}}$$$$density_{liquid} = \frac{(6.1 kg)(9.8 m/s^2) - 26 N}{(\frac{4}{3}\pi)(0.1 m)^3}$$$$density_{liquid} = 1500 kg/m^3$$

A 61-Kg Solid Sphere, Made of Metal Whose Density Is 2600