A compressive force is applied to a uniform rod of rectangular cross-section so that its length decreases by 1 \% . If the Poisson's ratio for the material of the rod be 0.2, which of the following statements is

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Correct answer: C. decreases by 0.6 \%

Given, Decrement in the length =1 \% Poisson's ratio for material of the rod, σ=0.2 As we know that, Volume, v=π r^ 2 l,[ where , l is the length of the rod ](Δ V)/(V)=(2 Δ r)/(r)+(Δ l)/(l)...( i) since, Poisson's ratio, σ=(-Δ D / D)/(Δ L / L)=(-Δ r / r)/(Δ L / L) So, Eq. (i) can be written as, aligned (Δ V)/(V)=(Δ l)/(l)(1-2 σ) (Δ V)/(V) ×100 &= ((Δ l)/(l) ×100)×(1-2 σ) &=-1 ×[1-2 ×(0.2)] &=-1 ×[1-0.4] &=-0.6 \% aligned Here, negative sign shows the decrement in the volume.

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