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.

A container has a large cylindrical lower part with a long thin cylindrical neck open at the top. The lower part of the container holds 14.8 m of water and the surface area of the bottom of the container is 5.90 m². The height of the lower part of the container is 2.50 m, and the neck contains a column of water 8.50 m high. The total volume of the column of water in the neck is 0.200 m³. What is the magnitude of the force exerted by the water on the bottom of the container?

In the process of loading a ship, a shipping container gets dropped into the water and sinks to the bottom of the harbor. Salvage experts plan to recover the container by attaching a spherical balloon to the container and inflating it with air pumped down from the surface. The dimensions of the container are 5.00 m long, 2.35 m wide, and 3.20 m high. As the crew pumps air into the balloon, its spherical shape increases and when the radius is 1.10 m, the shipping container just begins to rise toward the surface. Determine the mass of the container. You may ignore the weight of the balloon and the air in the balloon. The density of seawater is 1027 kg/m³. 434.54 X How does the weight of the container compare to the weight of the water displaced by the container and balloon when the container starts to rise? See if you can express the weight of the water displaced in terms of the density of the seawater and the dimensions of the container and balloon. kg Additional Materials

Consider a capillary tube in which water has risen. The contact angle is θ. The radius of the capillary tube is ‘r’. The surface tension is ‘S’. And the density of water is ‘ρ’. What is the expression for the height of water risen in the tube? Assume the radius of meniscus to be ‘R’. Let the height of water risen in the tube be ‘h’. a) 2Ssinθ / Rρg b) 2S / Rρg c) 2Scosθ / Rρg d) 2S / rρg

A solid which has a density of 2.7 g/cm3 has a cavity inside. When it is weighed in air, it is found to have a mass of 312 g and when immersed in water, its mass appears to be 160 g. What is the volume of the hidden cavity?

A cylindrical storage tank has a cross sectional area A1=1.5 m². The tank is set up vertically on the ground and filled with V=7.5 m³ of water. There is a valve at the bottom of the tank with an internal cross sectional area of 1.5 cm². What fraction of the total volume will be drained in the first 50 minutes after the valve is opened?

A spherical shell has an outside radius of 2.40 cm and an inside radius of a. The shell wall has uniform thickness and is made of a material with density 4.52 g/cm3. The space inside the shell is filled with a liquid having a density of 1.27 g/cm3. (a) Find the mass m of the sphere, including its contents, as a function of a. m = g (b) For what value of a does m have its maximum possible value? a = cm (c) What is this maximum mass? m = g (d) Explain whether the value from part (c) agrees with the result of a direct calculation of the mass of a solid sphere of uniform density made of the same material as the shell. (e) Would the answer to part (a) change if the inner wall were not concentric with the outer wall? Yes No

An object made of iron appears 300 N lighter in water than in air. The density of iron is equal to 7870 kgm-3 , and the density of water is 1000 kgm-3 . a) What is the volume of the object? b) What is the object’s weight in air?

A container has a large cylindrical lower part with a long thin cylindrical neck open at the top. The lower part of the container holds 19.5 m3 of water and the surface area of the bottom of the container is 7.80 m2. The height of the lower part of the container is 2.50 m, and the neck contains a column of water 8.50 m high. The total volume of the column of water in the neck is 0.200 m3. What is the magnitude of the force exerted by the water on the bottom of the container? in MN

The gauge pressure inside a soap bubble is 0.5 torr. If the surface tension in the soap film is 25 mN/m, what is the diameter of the soap? 0.99 um O 2.0 um O 1.5 mm O 3.0 mm