Question

A prismatic bar of volume V is subjected
to a tensile force in longitudinal direction.
If Poisson's ratio of the material is and
longitudinal strain is e, then the final
volume of the bar becomes
a) (1+e)(1-u)? V
b) (1-e)?( 1+ue) V
c) (1+e)(1-u e)? V
d) (1-ue) V
Please explain​

Answer 1

Answer:

(c) is the correct answer (1-e)(1+ue)^2 ×V

Answer 2

Answer:

The final volume of the bar becomes (l + e)(l-ne)2V

Explanation:

From the above question,

They have given :

A prismatic bar of volume V is subjected to a tensile force in longitudinal direction. If Poisson's ratio of the material is u and longitudinal strain is e, then the final volume of the bar becomes

A. (l + e)(l-u)2V

B. (l-e)2(l + ue)V

C. (l + e)(l-ne)2V

D. (l-ue)3V

The volume of the bar can be calculated using the formula V = A*L, where A is the cross-sectional area and L is the length of the bar. Since the bar is subjected to a tensile force in the longitudinal direction, the length of the bar will increase.

The change in length is given by the equation:

               ΔL = eL, where e is the longitudinal strain.

The new length of the bar is given by L' = (1 + e)L. Using the formula for volume, the new volume is given by V' = A*L' = A*(1 + e)L = (1 + e)2V.

Since the material has a Poisson's ratio u, the cross-sectional area of the bar will also change.

The change in area is given by the equation:

                     ΔA = -ueA.

The new area of the bar is given by A' = (1 - ue)A. Substituting this value into the equation for volume, the new volume of the bar becomes V' = A'*L' = (1 - ue)A*(1 + e)L = (1 + e)(1 - ue)2V.

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