Correct Answer - Option 1 : Modulus of rigidity of solids
CONCEPT:
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Viscosity is the property of fluid by virtue of which an internal force of friction comes into play when a fluid is in motion and which opposes the relative motion between its different layers.
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Viscosity is like friction which converts kinetic energy into heat energy.
- The coefficient of viscosity of liquids is analogous to the Modulus of rigidity of solids.
EXPLANATION:
- Unlike solids, the strain in a flowing liquid increases with time continuously.
- So for solids with an elastic modulus of rigidity, the shearing stress is proportional to the shear strain
- For fluids, it is proportional to the time rate of change of strain or strain rate.
- The coefficient of viscosity (η) of a fluid can be defined as the ratio of shearing stress to the strain rate.
η =\(\frac{F/A}{v/x}\) where v/x is dx.x/t ( velocity = dx/dt)=\(\frac{ Shearing stress}{Shear Strain/t} \)
Modulus of rigidity, η = \(\frac{F/A}{dx/x}\)=\(\frac{ Shearing stress}{Shear Strain} \)
- Thus the coefficient of viscosity of liquids is analogous to the modulus of rigidity of solids.
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Modulus of Rigidity state that within the elastic limit, the ratio of tangential stress to shear strain is called Modulus of Rigidity
Modulus of rigidity, η = \(\frac{F/A}{dx/x}\)=\(\frac{ Shearing stress}{Shear Strain} \)
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Shearing Stress is the internal restoring force set up per unit area of cross-section of the deformed body is called stress.
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Shearing Strain the ratio of change in length to the original length.
Shearing Stress= \(\frac{dx}{x}\)
