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ser-zykov [4K]
3 years ago
11

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 liqui

d of unknown density, the tension in the cord is 26 N. Find the density of the liquid.

Chemistry
1 answer:
deff fn [24]3 years ago
6 0

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

<u>Thus, the density of the liquid = 1470.43 kg/m³</u>

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