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The dimensional formula of Poisson's ratio is
1. [M0L-1T0]
2. [M0L2T0]
3. [M1L1T0]
4. [M0L0T0]

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Correct Answer - Option 4 : [M0L0T0]

The correct answer is option 4) i.e. [M0L0T0]

CONCEPT:

  • Poisson's ratio: It is defined as the ratio of transverse strain to longitudinal strain in the direction of the stretching force.
    • When a material is stretched in one direction, it tends to get compressed in the direction perpendicular to the direction of the force. 
    • Thus, a longitudinal strain causes a transverse strain and vice versa.
    • Poisson's ratio is positive for tensile deformation and negative for compressive deformation.

Poisson's ratio, \(\nu =- \frac{ϵ_t}{ϵ_l}\)

Where ϵt is the transverse strain and ϵis the longitudinal strain.

EXPLANATION:

  • Poisson's ratio is the ratio between transverse and longitudinal strain.
  • The strain is the ratio of two like quantities. Thus, the strain has no dimensions.
  • As a result, Poisson's ratio will be the ratio of two dimensionless quantities.
  • So, Poisson's ratio is dimensionless and its dimensional formula will be [M0L0T0].

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