Question

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.

Answer 1

Answer:

Density of the liquid = 1470.43 kg/m³

Explanation:

Given:

Mass of solid sphere(m) = 6.1 kg

Density of the metal = 2600 kg/m³

Thus volume of the liquid :

$Volume(V)=\frac{Mass(m)}{Density (\rho)}$

Volume of the sphere = 6.1 kg/2600 kg/m³ = 0.002346 m³

The volume of water displaced is equal to the volume of sphere (Archimedes' principle)

Volume displaced = 0.002346 m³

Buoyant force =$\rho\times gV$

Where

$\rho$ is the density of the fluid

g is the acceleration due to gravity

V is the volume displaced

The free body diagram of the sphere is shown in image.

According to image:

$mg=\rho\times gV+T$

Acceleration due to gravity = 9.81 ms⁻²

Tension force = 26 N

Applying in the equation to find the density of the liquid as:

$6.1\times 9.81=\rho\times 9.81\times 0.002346+26$

$33.841=\rho\times 9.81\times 0.002346$

$\rho=\frac{33.841}{9.81\times 0.002346}$

$\rho=1470.43 kgm^3$

Thus, the density of the liquid = 1470.43 kg/m³