A solid cylinder has a radius of 0.051 m and a height of 0.0030 m.The cylinder is composed of two different materials with mass densities of 1950 kg/m³ and 1470 kg/m³.The cylinder contains an equal mass m of each of the two materials,so that the total mass is M = 2m.What is the mass m? A)8.4 × 10^-² kg B)2.1 × 10^-² kg C)1.4 × 10^-² kg D)6.5 × 10^-² kg E)4.2 × 10^-² kg

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Quizplus · Accepted Answer

To find the mass $m$ of each material in the cylinder, we first calculate the total volume $V$ of the cylinder using the formula $V = \pi r^2 h$, where $r = 0.051$ m is the radius and $h = 0.0030$ m is the height. Substituting the given values, we get $V = \pi (0.051)^2 (0.0030) \approx 2.44 \times 10^{-5}$ m³.Given that the cylinder contains equal masses of two materials with densities $\rho_1 = 1950$ kg/m³ and $\rho_2 = 1470$ kg/m³, and the total mass is $M = 2m$, we can find the mass of each material by considering the average density $\bar{\rho}$ of the two materials, since the volume occupied by each material is the same.The average density $\bar{\rho}$ is given by $\bar{\rho} = \frac{\rho_1 + \rho_2}{2} = \frac{1950 + 1470}{2} = 1710$ kg/m³.The total mass $M$ can then be calculated using the formula $M = \bar{\rho} V$, which gives $M = 1710 \times 2.44 \times 10^{-5} \approx 4.17 \times 10^{-2}$ kg.Since $M = 2m$, we find that $m = \frac{M}{2} = \frac{4.17 \times 10^{-2}}{2} \approx 2.1 \times 10^{-2}$ kg, which corresponds to choice B.

A Solid Cylinder Has a Radius of 0