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

Question

8 days ago

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

1 answer:

castortr0y [923] · Answer 1 · 2026-02-25T09:50:00+03:00

Answer:

The calculated density of the liquid is 1470.43 kg/m³.

Explanation:

Given:

Mass of the solid sphere (m) = 6.1 kg

Density of the metal = 2600 kg/m³

To find the volume of the liquid:

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

Volume of the sphere can be calculated as 6.1 kg / 2600 kg/m³ = 0.002346 m³.

According to Archimedes' principle, the volume of water displaced is equal to the volume of the sphere.

Volume displaced = 0.002346 m³

The buoyant force formula is: $\rho\times gV$

Where:

$\rho$ is the fluid's density,

g represents the acceleration due to gravity,

V indicates the volume displaced.

Referencing the free-body diagram of the sphere shown in the image:

$mg=\rho\times gV+T$

Acceleration due to gravity = 9.81 ms⁻²

Tension force = 26 N

Using these in the equation to ascertain the liquid density yields:

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

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

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

$\rho=1470.43 kgm^3$

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