Correct Answer - Option 4 : Strain
CONCEPT:
Dimensions:
- When a derived quantity is expressed in terms of fundamental quantities, it is written as a product of different powers of the fundamental quantities.
- The powers to which fundamental quantities must be raised in order to express the given physical quantity are called its dimensions.
- A quantity without dimension will usually be a ratio of two quantities with similar dimensions and hence, will cancel out. Thus, they will have no units and are known as dimensionless quantities.
EXPLANATION:
Velocity:
- The rate of change of displacement of a body is called the velocity of that body.
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Velocity is a vector quantity that has both magnitudes as well as direction.
- The unit of velocity is m/s and the dimension of velocity is [M0LT-1].
Viscosity:
- The state of being sticky, thick, and semi-fluid in consistency, due to internal friction is called viscosity.
- The SI unit of viscosity is newton-second per square meter (N·s/m2).
Strain:
- The ratio of change in configuration to the original configuration is called strain.
\({\rm{strain}} = \frac{{{\rm{Change\;in\;dimension}}}}{{{\rm{Original\;dimension}}}}\)
- As the strain is the ratio of two like quantities, it has no units and no dimensions.
- and has no dimension.
- Its dimension can be expressed as M0L0T0.
Stress:
- Stress is the ratio of the load or force to the cross-sectional area of the material to which the load is applied.
\(Stress = \frac{{Force{\rm{\;}}\left( F \right)}}{{Area{\rm{\;}}\left( A \right)}} = N{m^{ - 2}}\)
- The standard unit of stress is N/m2.
