Question

A sphere completely submerged in water is tethered to the bottom with a string. The tension in the string is one-fourth the weight of the sphere.

What is the density of the sphere?

Answer 1

ρ = 800 kg/m³

Step-by-step explanation:

Let the volume of the sphere = V

and the density of the sphere = ρ

density of water , ρ_w = 1000 Kg/m^3

tension in the string is one-fourth the weight of the sphere.

Tension in the rope ,

`T = \rho V (g)/(4)`

for the sphere to in equilibrium

T + Weight = buoyant force

`\rho V(g)/(4) + \rho V g = \rho_w V g`

`(\rho)/(4)+\rho= \rho_w`

`(5\rho)/(4)= 1000`

ρ = 800 kg/m³

density of the sphere is equal to 800 kg/m³