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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
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Short Answer

A -tall, -diameter plastic tube has a sealed bottom. of lead pellets are poured into the bottom of the tube, whose mass is , then the tube is lowered into a liquid. The tube floats with extending above the surface. What is the density of the liquid?

Therefore the mass of the rock is

See the step by step solution

Step by Step Solution

Step : 1 Introduction 

Archimedes principle states that the upward force acts on the object when an object partly or fully immersed in a fluid. This force is called buoyant force. Mathematically, the buoyant force can be expressed as,

Here, is the density of fluid, is volume of displaced fluid, and is acceleration due to gravity.

Step :2 Explanation 

Let be the radius of the hemisphere. The diameter of the hemisphere is . Thus, the radius of the hemisphere is,

The volume of the hemisphere is half of the sphere. Thus, the volume of hemisphere is,

Substitute in above equation

Step :3 Weight of the rock 

The weight of the rock and the hemisphere bowl

Here, is the mass of the rock, is the mass of the hemisphere, and is the acceleration due to gravity.

After the rock is placed in the bottom of a plastic boat with maximum weight, the hemisphere gets totally dipped in the water without sinking it, and the water level is just in level with the hemisphere. So, the total buoyant force exerted on the hemisphere is equal to the total weight of the system of rock and the hemisphere bowl. Thus.

Substitute in above equation

Rewrite the equation in

Substitute in above equation

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