A palindrome is a number or a text phrase that reads the same backwards as forwards. For example, each of the following five-digit integers is a palindrome: 12321, 55555, 45554 and 11611. Write a C++ program that reads in a five-digit integer and determines whether it is a palindrome .

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 Step 1

Given data:

Solid shaft diameter (d) = 60 mm = 0.06 m

Determine,

Shear stress at points A and B

$\mathrm{1 }. {\mathrm{\tau }}_A$

$\mathrm{2 }. {\mathrm{\tau }}_B$

Step 2

We know that, from torsion equation

$\frac{\mathrm{T }}{\mathrm{J }}= \frac{\mathrm{\tau }}{R}$

$\mathrm{\tau }= \frac{\mathrm{T }}{\mathrm{J }}\times R$

Where,

$\mathrm{\tau }=$shear stress, N/m ²

$\mathrm{T }=$Torque, N.m

$\mathrm{R }=$Radius, m

$\mathrm{J }=$Polar moment of inertia, m ⁴

^{$\mathrm{J }= \frac{\mathrm{\pi }}{\mathrm{2 }}\times {\mathrm{d }}^{\mathrm{4 }}{\mathrm{m }}^4$}

^{$\mathrm{J }= \frac{\mathrm{\pi }}{\mathrm{2 }}\times {( \mathrm{0 }. \mathrm{06 }\mathrm{m }) }^{\mathrm{4 }}= \mathrm{2 }. \mathrm{03 }\times {\mathrm{10 }}^{- \mathrm{5 }}{\mathrm{m }}^4$}

Step 3

From the diagram

$$\begin{gathered} {\mathrm{\tau }}_{\mathrm{A }\mathrm{C }}= \mathrm{400 }\mathrm{N }. \mathrm{m } \\ {\mathrm{\tau }}_{\mathrm{AC }}= \mathrm{200 }\mathrm{N }. \mathrm{m }( \mathrm{600 }\mathrm{N }. \mathrm{m }- \mathrm{400 }\mathrm{N }. \mathrm{m }) \end{gathered}$$

${\mathrm{\tau }}_{\mathrm{A }}= \frac{{\mathrm{T }}_{\mathrm{A }\mathrm{C }}}{\mathrm{J }}\times \mathrm{R }\mathrm{N }/ {\mathrm{m }}^2$

${\mathrm{\tau }}_{\mathrm{A }}= \frac{\mathrm{400 }\mathrm{N }. \mathrm{m }}{\mathrm{2 }. \mathrm{03 }\times {\mathrm{10 }}^{- \mathrm{5 }}{\mathrm{m }}^{\mathrm{4 }}}\times \mathrm{0 }. \mathrm{03 }\mathrm{m }\mathrm{N }/ {\mathrm{m }}^2$

${\mathrm{\tau }}_{\mathrm{A }}= \mathrm{591133 }\mathrm{N }/ {\mathrm{m }}^{\mathrm{2 }}= \mathrm{591 }. \mathrm{133 }\mathrm{kN }/ {\mathrm{m }}^2$

${\mathrm{\tau }}_{\mathrm{B }}= \frac{{\mathrm{T }}_{\mathrm{B }\mathrm{C }}}{\mathrm{J }}\times \mathrm{R }\mathrm{N }/ {\mathrm{m }}^2$

${\mathrm{\tau }}_{\mathrm{B }}= \frac{\mathrm{200 }\mathrm{N }. \mathrm{m }}{\mathrm{2 }. \mathrm{03 }\times {\mathrm{10 }}^{- \mathrm{5 }}{\mathrm{m }}^{\mathrm{4 }}}\times \mathrm{0 }. \mathrm{03 }\mathrm{m }\mathrm{N }/ {\mathrm{m }}^2$

${\mathrm{\tau }}_{\mathrm{B }}= \mathrm{295566 }. \mathrm{5 }\mathrm{N }/ {\mathrm{m }}^2$

${\mathrm{\tau }}_{\mathrm{B }}= \mathrm{295 }. \mathrm{566 }\mathrm{kN }/ {\mathrm{m }}^2$

The Shear stresses at Point A and B are

${\mathrm{\tau }}_{\mathrm{A }}= \mathrm{591 }. \mathrm{133 }\mathrm{kN }/ {\mathrm{m }}^2$

${\mathrm{\tau }}_{\mathrm{B }}= \mathrm{295 }. \mathrm{566 }\mathrm{kN }/ {\mathrm{m }}^2$

Step 4

The shear stress on volume elements are