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Determining Oil & Ball Bearing Density: Physics Explained

Chapter 1, Problem 1.98

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QUESTION:

A graduated cylinder is filled to the 40.00-mL mark with a mineral oil. The masses of the cylinder before and after the addition of the mineral oil are 124.966 g and 159.446 g, respectively. In a separate experiment, a metal ball bearing of mass 18.713 g is placed in the cylinder and the cylinder is again filled to the 40.00-mL mark with the mineral oil. The combined mass of the ball bearing and mineral oil is 50.952 g. Calculate the density and radius of the ball bearing. [The volume of a sphere of radius r is \((4 / 3) \pi r^{3}\).]

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Determining Oil & Ball Bearing Density: Physics Explained
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Discover how to determine the density of mineral oil and a metal ball bearing using a graduated cylinder. Learn the method of calculating the mass difference and volume to deduce the density and radius of the ball. Watch a detailed physics experiment explained step by step.

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Questions & Answers

QUESTION:

A graduated cylinder is filled to the 40.00-mL mark with a mineral oil. The masses of the cylinder before and after the addition of the mineral oil are 124.966 g and 159.446 g, respectively. In a separate experiment, a metal ball bearing of mass 18.713 g is placed in the cylinder and the cylinder is again filled to the 40.00-mL mark with the mineral oil. The combined mass of the ball bearing and mineral oil is 50.952 g. Calculate the density and radius of the ball bearing. [The volume of a sphere of radius r is \((4 / 3) \pi r^{3}\).]

ANSWER:

Step 1 of 5

Here, we are going the density and radius of the ball bearing.

Given that,

Mass of the cylinder without oil M = 124.966 g

Mass of the cylinder with oil \(M_{O}=159.446 \mathrm{~g}\)

Therefore,

Mass of the Oil \(=\left(M_{O}-M\right)=(59.446-124.966) \mathrm{g}=34.480 \mathrm{~g}\)

Thus,

Density of the oil = Mass/Volume

= (34.480 g/40.00 mL)

= 0.8620 g/mL

Final density of the oil is found as 0.8620 g/mL

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