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Physics Question on Stress and Strain

A force is applied to a steel wire ' AA ', rigidly clamped at one end As a result elongation in the wire is 02 mm02\, mm If same force is applied to another steel wire ' BB ' of double the length and a diameter 2424 times that of the wire ' AA ', the elongation in the wire ' BB ' will be (wires having uniform circular cross sections)

A

2.77×10−2mm2.77 \times 10^{-2} mm

B

6.9×10−2mm6.9 \times 10^{-2} mm

C

6.06×10−2mm6.06 \times 10^{-2} mm

D

3.0×10−2mm3.0 \times 10^{-2} mm

Answer

6.9×10−2mm6.9 \times 10^{-2} mm

Explanation

Solution

The correct answer is (B) : 6.9×10-2 mm
Y=ℓΔℓ​F/A​
⇒F=ℓYA​Δℓ
(ℓAΔℓ​)1​=(ℓAΔℓ​)2​
⇒Δℓ1​Δℓ2​​=A2​A1​​×ℓ1​ℓ2​​
⇒0.2Δℓ2​​=2.4×2.41​×12​
⇒Δℓ2​=6.9×10−2mm