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8.Mechanical Properties of Solids
medium
આકાર વિકૃતિ $\phi$ ના લીધેં પદાર્થના કદ $V$ માં સંગ્રહ થતી. વિકૃતિ ઉર્જા કેટલી ? (shear modulus is $\eta$ )
A
$\frac{\phi^2 V}{2 \eta}$
B
$\frac{\phi V^2}{2 \eta}$
C
$\frac{\phi^2 v}{\eta}$
D
$\frac{1}{2} n \phi^2 V$
Solution
(d)
Shear modulus $=\frac{\text { Shear } \text { stress }}{\text { Shear } \text { stress }}$
$\eta=\frac{\text { Shear stress }}{\phi}$
$\eta \phi=$ Shear stress
Strain energy per unit volume $=\frac{1}{2} \times$ shear stress $\times$ shear strain $\Rightarrow \frac{\text { Strain energy }}{\text { Volume }}=\frac{1}{2} \times \eta \phi \times \phi \quad$ (Cross multiply volume)
Strain energy $=\frac{1}{2} \eta \phi^2 V$
Standard 11
Physics
