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Chapter 14: Q. 19 (page 384)

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

Short Answer

Expert verified

The density of the sphere if tension within the string is one-third the load of the sphere, ρb=750kg/m3

Step by step solution

01

Newton's first law.

The law of inertia, often referred to as Newton's first law, states that if a body is at rest or occupation a line at a relentless speed, it will remain at rest or still move in an exceedingly straight path at a continuing speed until it's acted with by a force.

02

Derive the Force.

Using the information provided within the exercise and Newton's first law, with the positive direction upwards, we will write:

FB-T-Fg=0⇒FB=FG+T=43mg

03

Find the density.

Knowing the buoyant force formula and expressing the ball's mass asm=ρbV, we may write:

ρwgV=43ρbVg⇒ρb=34ρw

Because we all know the density of water, we will calculate the numerical solution as,

ρb=34×1000=750kg/m3

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