2 Materials have a measurable property known as the Young's Modulus, E.
If a force is applied to one face of a block of the material then the material is stretched by a distance called the extension. Young's modulus is defined as the ratio \(\frac { \text { Stress } } { \text { Strain } }\) where Stress is defined as the force per unit area and Strain is the ratio of the extension of the block to the length of the block.

1. Show that Strain is a dimensionless quantity.
2. By considering the dimensions of both Stress and Strain determine the dimensions of \(E\). It is suggested that the speed of sound in a material, \(c\), depends only upon the value of Young's modulus for the material, \(E\), the volume of the material, \(V\), and the density (or mass per unit volume) of the material, \(\rho\).
3. Use dimensional analysis to suggest a formula for \(c\) in terms of \(E , V\) and \(\rho\).
4. The speed of sound in a certain material is \(500 \mathrm {~ms} ^ { - 1 }\).
   1. Use your formula from part (c) to predict the speed of sound in the material if the value of Young’s modulus is doubled but all other conditions are unchanged.
   2. With reference to your formula from part (c), comment on the effect on the speed of sound in the material if the volume is doubled but all other conditions are unchanged.
5. Suggest one possible limitation caused by using dimensional analysis to set up the model in part (c).