A rectangular metallic block of dimensions $40 \mathrm{~mm} \times 20 \mathrm{~mm}$ when pulled with a…

A rectangular metallic block of dimensions $40 \mathrm{~mm} \times 20 \mathrm{~mm}$ when pulled with a tension of $50 \mathrm{kN}$ undergoes only elastic deformation. The strain in the block is (The shear modulus of the material of the block is $40 \times 10^9 \mathrm{Nm}^{-2}$ )
  1. $1.56 \times 10^{-3} \mathrm{~m}$
  2. $2.4 \times 10^{-3} \mathrm{~m}$
  3. $3.2 \times 10^{-3} \mathrm{~m}$
  4. $1.08 \times 10^{-3} \mathrm{~m}$

Solution

Tension, $\mathrm{F}=50 \times 10^3 \mathrm{~N}$ Area, $A=40 \times 20 \times 10^{-6} \mathrm{M}$ $\begin{aligned} & \text { Modulus of the material }=\frac{\text { Stress }}{\text { Strain }} \\ & \text { Strain }=\frac{\text { Force }}{\text { Area } \times \text { shear modulus }}\end{aligned}$ $=\frac{50 \times 10^3}{40 \times 20 \times 10^{-6} \times 40 \times 10^9}=1.5 \times 10^{-3} \mathrm{~m}$

Asked in: AP EAMCET 2023 (17 May Shift 2)

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