Question

Compare the ratio of increase in volumes of a thin cylinder to that of a spherical shell having the same internal pressure and $\frac{d}{t}$ ratio, where d and t are internal diameter and the thickness respectively. Take $\mu =0.3$.

• A. 2
• B. 1.81
• C. 3.4
• D. 2.89

Answer 1

The correct option is B 1.81

For cylinder, increase in volume, $\delta V=V.({\in }_l+2{\in }_c)$
$=\frac{V}{E}.\frac{pd}{4t}\left[\left(\right(1-2\left(0.3\right))+2(2-(1\times 0.3)\left)\right)\right]$

$=\frac{V}{E}.\frac{3.8pd}{4t}$

For spherical shell, $\delta V^{\prime }=\frac{V}{E}.\frac{pd}{4t}\left[\right(1-0.3)+2(1-0.3\left)\right]$

$=\frac{V}{E}2.1\frac{pd}{4t}$

$\therefore =\frac{\delta V}{\delta V^{\prime }}=\frac{3.8}{2.1}=1.81$