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Chapter 1: Problem 3

When a marble is dropped into a beaker of water, it sinks to the bottom. Which of the following is the best explanation? a, The surface area of the marble is not large enough to be held up by the surface tension of the water. b. The mass of the marble is greater than that of the water. c. The marble weighs more than an equivalent volume of the water. d. The force from dropping the marble breaks the surface tension of the water. e. The marble has greater mass and volume than the water. Justify your choice, and for choices you did not pick, explain what is wrong about them.

Short Answer

Expert verified
The correct answer is option c. The marble sinks because its weight (mass x gravity) is greater than the weight of an equivalent volume of water, meaning it is denser than the water. Option A is incorrect because surface area does not affect sinking or floating; it depends on an object's density. Option B is wrong since mass alone does not determine whether an object sinks or floats; it depends on density. Option D is incorrect because although dropping the marble breaks the surface tension, that is not the main reason it sinks. Finally, option E is wrong as it's not the absolute values of mass and volume that matter, but their ratios, which define an object's density.

Step by step solution

01

Identify the Correct Option

The correct answer is option c. The marble sinks to the bottom of the beaker because its weight (mass x gravity) is greater than the weight of an equivalent volume of water. This means that the marble is denser than the water, causing it to sink.
02

Explanation for Option A

Option A is incorrect because it suggests that the marble would not sink if it had a larger surface area. Surface area does not affect whether an object sinks or floats in a liquid. What matters is the object's density in comparison to the liquid.
03

Explanation for Option B

Option B is incorrect because it states that the mass of the marble is greater than the mass of water. The mass of the marble does not determine whether it sinks or floats; it is the relative density of the marble and water that matters. It's possible that a massive floating object (like a ship) has a greater overall mass than the water it displaces, yet it still floats because its average density is less than the water's.
04

Explanation for Option D

Option D is incorrect because it suggests that the force from dropping the marble breaks the surface tension of the water, causing the marble to sink. Though it's true that dropping the marble breaks the surface tension, this isn't the primary reason why the marble sinks. The marble sinks due to its density relative to the water, not because of any interaction with surface tension.
05

Explanation for Option E

Option E is incorrect because the claim that the marble "has greater mass and volume than the water" is not enough to explain why it sinks. A larger object might have a greater mass and volume, but it would still float if its average density is less than that of water. It's not the absolute values of mass and volume that determine whether an object sinks or floats, but their ratios, which define an object's density.

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Most popular questions from this chapter

Perform the following mathematical operations, and express the result to the correct number of significant figures. a. \(\frac{2.526}{3.1}+\frac{0.470}{0.623}+\frac{80.705}{0.4326}\) b. \((6.404 \times 2.91) /(18.7-17.1)\) c. \(6.071 \times 10^{-5}-8.2 \times 10^{-6}-0.521 \times 10^{-4}\) d. \(\left(3.8 \times 10^{-12}+4.0 \times 10^{-13}\right) /\left(4 \times 10^{12}+6.3 \times 10^{13}\right)\) e. \(\frac{9.5+4.1+2.8+3.175}{4}\) (Assume that this operation is taking the average of four numbers. Thus 4 in the denominator is exact.) f. \(\frac{8.925-8.905}{8.925} \times 100\) (This type of calculation is done many times in calculating a percentage error. Assume that this example is such a calculation; thus 100 can be considered to be an exact number.)

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