Question

On all the six surfaces of a unit cube, equal tensile force of F is applied. The increase in length of each side will be (Y = Young's modulus, σ = Poisson’s ratio) 

(1) F/Y(1 −σ)  

(2) F/ Y(1 +σ) 

(3) F(1 − 2σ)/Y

(4) F/ Y(1 +2σ) 

Answer 1

Correct option (3) F(1 − 2σ)/Y

Explanation:

Tensile strain on each face Y/ F

Lateral strain due to the other two forces acting on perpendicular faces= −2σF/Y

 Total increase in length = (1 − 2σ)F/Y