Let Pa represent the density of aluminum and Pf that of iron. Find an expression of the radius (ra ) of a solid aluminum sphere that balances a solid iron sphere of radius rf on an equal-arm balance

Need Help: It is known that a cubical object made of cast aluminum 0.213 m on a side contains a hollow cavity also in the shape of a cube but of unknown dimensions. If the mass of the object is 22.8 kg, determine the length of each side of the interior cubical cavity. The density of aluminum is 2.70  103 kg/m3. Given Tip: How is the volume of the cubical object related to the volume of aluminum in the object and the volume of the cubical cavity? How is the mass of the cubical object related to the mass of aluminum in the object? Recall how the volume of a cube is related to the length of each side of the cube.

An automobile tire is shown in the figure below. The tire is made of rubber with a uniform density of 1.10 × 103 kg/m³. The tire can be modeled as consisting of two flat sidewalls and a tread region. Each of th sidewalls has an inner radius of 16.5 cm and an outer radius of 30.5 cm as shown, and a uniform thickness of 0.675 cm. The tread region can be approximated as having a uniform thickness of 2.50 cm (that i its inner radius is 30.5 cm and outer radius is 33.0 cm as shown) and a width of 19.4 cm. What is the moment of inertia (in kg m2) of the tire about an axis perpendicular to the page through its center? " 33.0 cm 16.5 cm Sidewall 30.5 cm Tread Enter a number. find the moment of inertia of the sidewall and the moment of inertia of the tread region. Each can be modeled as a cylinder of nonzero thickness. What is the inner and outer radius for each case? What is the formula for the moment of inertia for a thick-walled cylinder? How can you find the mass of a hollow cylinder?…

To verify her suspicion that a rock specimen is hollow, a geologist weighs the specimen in air and in water. She finds that the specimen weighs twice as much in air as it does in water. The density of the solid part of the specimen is 6.22 × 10³ kg/m³. What fraction of the specimen's apparent volume is solid? Number i Units

Calculate the mass of a solid gold rectangular bar that has dimensions Iwh = 4.80 cm x 12.0 cm x 25.0 cm. (The density of gold is 19.3 x 103 kg/m³.) kg

A sphere made of either brass or aluminum has a radius r= 10cm. What is its mass?

Problem 1: Suppose you have a coffee mug with a circular cross section and vertical sides. What is its inside radius if it holds 375 g of coffee when filled to a depth of 7.5 cm? Assume coffee has the same density as water, 10³ kg/m³.

Question 6: Suppose you have a coffee mug with a circular cross-section and vertical sides. What is its inside radius in cm if it holds 375 g of coffee when filled to a depth of 7.5 cm? Density of coffee is 1000 kg/m³. Unit conversion: 1 kg = 1000 g; 1 m = 100 cm.

To verify her suspicion that a rock specimen is hollow, a geologist weighs the specimen in air and in water. She finds that the specimen weighs twice as much in air as it does in water. The density of the solid part of the specimen is 3.96 × 10³ kg/m³. What fraction of the specimen's apparent volume is solid? Number i Units

A scanning electron micrograph of xylem vessels in a corn root shows the vessels magnified by a factor of 598. In the micrograph the xylem vessel is 2.80 cm in diameter. a. What is the diameter of the vessel itself? b. By what factor has the cross-sectional area of the vessel been increased in the micrograph?