“Y stretches, B squeezes, G slides”
Which modulus goes with which deformation
Young's for a pulled wire, bulk for pressure from all sides, shear for a face pushed sideways. Pick the modulus by what is being done to the body.
Class 11 Physics · Gujarat Board, CBSE, GUJCET and JEE
Mechanical Properties of Solids formulas
This short chapter is mostly one idea, stress over strain, wearing three different names. It is worth learning properly because the stress-strain graph is asked as a theory question almost every year, and the numerical work is straightforward marks.
12 formulas, 3 memory hooks, and the 5 mistakes that cost the most marks.
Stress and strain
| What | Formula | Symbols and notes |
|---|---|---|
| Stress | σ = F/A | unit N m−2 or pascal, same unit as pressure |
| Longitudinal strain | ε = ΔL/L | a ratio, so no unit |
| Volume strain | ΔV/V | used for the bulk modulus |
| Shear strain | θ = Δx/L | the angle through which a face is tilted |
The three moduli
| What | Formula | Symbols and notes |
|---|---|---|
| Young's modulus | Y = stress/strain = FL/(AΔL) | for stretching a wire |
| Bulk modulus | B = −pV/ΔV | for uniform compression; the minus keeps B positive |
| Shear modulus | G = F/(Aθ) | also called the modulus of rigidity |
| Compressibility | K = 1/B | how easily a material is squeezed |
| Poisson's ratio | ν = (Δd/d)/(ΔL/L) | lateral strain over longitudinal strain, between 0 and 0.5 |
Energy stored
| What | Formula | Symbols and notes |
|---|---|---|
| Elastic potential energy | U = ½ × stress × strain × volume | the area under the stress-strain curve |
| In terms of extension | U = ½ FΔL = ½ (YA/L)(ΔL)² | a stretched wire behaves like a spring of constant YA/L |
| Energy density | u = ½ × stress × strain | energy stored per unit volume |
Taught by Darshit Bhatt, founder and lead faculty at Darshit Sir Institute. Instrumentation and Control engineer, with a master's degree and a chartered degree, teaching in Paldi, Ahmedabad since 2006.
Know the formula but not when to use it?
Darshit Sir has taught this in Paldi since 2006, in the classroom and live online.
Memory hooks
How to remember this chapter.
“Steel is stiffer, rubber is stretchier”
What a large Y means
A large Young's modulus means hard to stretch, not strong. Steel has a Y about 100,000 times rubber's, which is why bridges are not built of rubber.
“Elastic limit, then no return”
Reading the stress-strain graph
Up to the elastic limit the wire returns to its original length. Past the yield point it stays deformed, and at the breaking point it snaps.
Where marks go
The mistakes that cost the most.
- Calling stress the same as pressure. They share a unit, but stress can be shear or tensile, and pressure cannot.
- Giving strain a unit. It is a ratio of two lengths, so it has none.
- Forgetting the factor of ½ in the stored energy. The force grows from zero, so the average force does the work.
- Using Young's modulus where the body is squeezed from all sides. That is the bulk modulus.
- Thinking a larger Young's modulus means a stronger material. It means a stiffer one.
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