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Moment of Inertia of a Disc

In a thin cyl...

Question

In a thin cylindrical shell, the ratio of longitudinal stress to hoop stress is

A

0.5

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B

1.0

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C

1.5

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D

2.0

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Solution

The correct option is A 0.5
In a thin cylindrical shell,

$L o n g i t u d i n a l s t r e s s (σ_{l}) = \frac{P d}{4 t}$

$H o o p s t r e s s (σ_{h}) = \frac{P d}{2 t}$

Ratio,
$\frac{σ_{l}}{σ_{h}} = \frac{P d / 4 t}{P d / 2 t} = \frac{1}{2} = 0.5$

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