Question

The material of a rubber balloon has Poisson's ratio of 0.5. If uniform pressure is applied to blow the balloon, the volumetric strain of the material will be-
1. 0.20
2. 0.25
3. 0.50
4. Zero

Answer 1

Correct Answer - Option 4 : Zero

Concept:

Volumetric strain \(= \frac{{{\sigma _x} + {\sigma _y} + {\sigma _z}}}{E}\left( {1 - 2\mu } \right)\)

For uniaxial, volumetric strain \(= \frac{\sigma }{E}\left( {1 - 2\mu } \right) = e\left( {1 - 2\mu } \right)\)

Calculation:

Volumetric strain \(= \frac{{{\sigma _x} + {\sigma _y} + {\sigma _z}}}{E}\left( {1 - 2\times0.5 } \right)=0\)