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Chapter 14: Q. 6 (page 383)

Rank in order, from largest to smallest, the densities of blocks a, b, and c in FIGURE Q14.6. Explain.


Short Answer

Expert verified

Density in descending order is ρa> ρc > ρb

Step by step solution

01

Given information

Given figure shows three blocks floating in liquid.

02

Explanation

We know that buoyant force acting on a mass floating in a liquid depends on density or object, submerged volume of object and gravity.

Fbuoyant=Vsρg

Lets assume three blocks are floating have Volume Va, Vb and Vcand density ρa, ρband ρc

Then

Vsaρg=Vaρag⇒ρa=VsaVaρVsbρg=Vbρbg⇒ρb=VsbVbρVscρg=Vcρcg⇒ρc=Vs-cVcρ

So density depends on the ratio of submerged volume to the total volume.

From the figure we can see that

VS-aVa>VS-cVc>VS-bVb

This means the densities are in the order

ρa> ρc > ρb

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Most popular questions from this chapter

A nuclear power plant draws 3.0×106L/min of cooling water from the ocean. If the water is drawn in through two parallel,3.0−m-diameter pipes, what is the water speed in each pipe?

What is the volume in mL of 55 g of a liquid with density 1100 kg/m3?

FIGURE Q14.4 shows two rectangular tanks, A and B, full of water. They have equal depths and equal thicknesses (the dimension into the page) but different widths.

a. Compare the forces the water exerts on the bottoms of the tanks. Is FA larger than, smaller than, or equal to FB? Explain.
b. Compare the forces the water exerts on the sides of the tanks. Is FA larger than, smaller than, or equal to FB? Explain.

The 1.0−m-tall cylinder in FIGURE P14.61 contains air at a pressure of 1atm. A very thin, frictionless piston of negligible mass is placed at the top of the cylinder, to prevent any air from escaping, then mercury is slowly poured into the cylinder until no more can be added without the cylinder overflowing. What is the height h of the column of compressed air?

Hint: Boyle's law, which you learned in chemistry, says p1V1=p2V2 for a gas compressed at constant temperature, which we will assume to be the case.

An object has density ρ.
a. Suppose each of the object’s three dimensions is increased by a factor of 2 without changing the material of which the object is made. Will the density change? If so, by what factor? Explain.
b. Suppose each of the object’s three dimensions is increased by a factor of 2 without changing the object’s mass. Will the density change? If so, by what factor? Explain.
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