Q.22

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Found in: Page 384

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

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# A , steel cylinder floats in mercury. The axis of the cylinder is perpendicular to the surface. What length of steel is above the surface

Length of steel cylinder above the surface is

See the step by step solution

## Step 1: Expression for buoyant force

The cylinder floats in the mercury bath. So, the net force on it is zero. Use the expression for buoyant force and gravitational force and equate them to calculate the length of the steel above the surface.

The expression for buoyant force is,

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

## Step 2: Figure shows the situation

The following figure shows the situation.

Here, is the length of the cylinder above the surface.

## Step 3: Calculation of volume

The buoyant force on the cylinder submerged in Mercury is,

From Archimedes principle, the buoyant force acting an the steel cylinder is equal to weight of the cylinder submerged and it is expressed as follows:

Here, is volume of the cylinder.

Combine the above two equations.

The volume of the displaced fluid is,

.

## Step 4: Calculation of length

Replaceby , by in and rearrange the expression for .

Substitute for, for ,

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