Question
Define the following quantities and write their units-strain, stress, modulus of elasticity.
✓
Answer
(i) Strain : If more than one external force appears on an object, then its size, length, area, volume or shape may be changed. This change is called strain. It is measured by the fractional change in the size of the structure. Hence
$\begin{aligned} \text { Longitudinal strain } & =\frac{\text { Change in length }}{\text { Original length }} \\ \text { Surface strain } & =\frac{\text { Change in area }}{\text { Original area }} \\ \text { Volume strain } & =\frac{\text { Change in volume }}{\text { Original volume }}\end{aligned}$
It has no unit.
(2) Stress : When any object is deformed, due to inter-molecular forces (attraction or repulsion) such restoring forces are produced which try to restore the shape/size of the object. These elastic forces and they are measured by the elastic force produced per unit area of the surface on which this force is applied. Therefore,
$\begin{array}{l}\text { Stress }=\frac{\text { Restoring force }}{\text { Surface area }} \\ \text { Stress }=\text { F } / A \end{array}$
In equilibrium state, the value of internal restoring force is equal to the external force. The unit of stress is N/m2
(3) (3) Modulus of elasticity Within elastic limit, stress is directly proportional to the strain i.e. stress oc strain.
or $\quad \frac{\text { Stress }}{\text { Strain }}=$ Constant $(E)$
This constant (E) is called coefficient of elasticity of the material. Since there is no unit of strain, hence unit of co-efficient of elasticity is Newton $/ m ^2$.
Young's Modulus of elasticity : The ratio of longitudinal stress and longitudinal strain is called Young's Modulus of elasticity of the material of the wire.
$\begin{array}{l} Y =\frac{\text { Longitudinal stress }}{\text { Longitudinal strain }}=\frac{ F / A }{\frac{\Delta L }{ L }} \\ Y =\frac{ FL }{ A \Delta L }\end{array}$
$\begin{aligned} \text { Longitudinal strain } & =\frac{\text { Change in length }}{\text { Original length }} \\ \text { Surface strain } & =\frac{\text { Change in area }}{\text { Original area }} \\ \text { Volume strain } & =\frac{\text { Change in volume }}{\text { Original volume }}\end{aligned}$
It has no unit.
(2) Stress : When any object is deformed, due to inter-molecular forces (attraction or repulsion) such restoring forces are produced which try to restore the shape/size of the object. These elastic forces and they are measured by the elastic force produced per unit area of the surface on which this force is applied. Therefore,
$\begin{array}{l}\text { Stress }=\frac{\text { Restoring force }}{\text { Surface area }} \\ \text { Stress }=\text { F } / A \end{array}$
In equilibrium state, the value of internal restoring force is equal to the external force. The unit of stress is N/m2
(3) (3) Modulus of elasticity Within elastic limit, stress is directly proportional to the strain i.e. stress oc strain.
or $\quad \frac{\text { Stress }}{\text { Strain }}=$ Constant $(E)$
This constant (E) is called coefficient of elasticity of the material. Since there is no unit of strain, hence unit of co-efficient of elasticity is Newton $/ m ^2$.
Young's Modulus of elasticity : The ratio of longitudinal stress and longitudinal strain is called Young's Modulus of elasticity of the material of the wire.
$\begin{array}{l} Y =\frac{\text { Longitudinal stress }}{\text { Longitudinal strain }}=\frac{ F / A }{\frac{\Delta L }{ L }} \\ Y =\frac{ FL }{ A \Delta L }\end{array}$
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