Two wires of same length and radius are joined end to end and loaded. The Young's modulii of the materials of the two wires are Y? and Y?. The combination behaves as a single wire then its Young's modulus is :
Two wires of same length and radius are joined end to end and loaded. The Young's modulii of the materials of the two wires are Y? and Y?. The combination behaves as a single wire then its Young's modulus is :
Option 1 -
Y = (Y₁Y₂) / (2(Y₁ + Y₂))
Option 2 -
Y = (2Y₁Y₂) / (3(Y₁ + Y₂))
Option 3 -
Y = (Y₁Y₂) / (Y₁ + Y₂)
Option 4 -
Y = (2Y₁Y₂) / (Y₁ + Y₂)
Asked by Shiksha User
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1 Answer
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Correct Option - 4
Detailed Solution:Y? = (F/A) / (Δl? /l)
Y? = (F/A) / (Δl? /l)
Y = (F/A) / (Δl? + Δl? )/ (2l)
= (F/A) / ( (1/2) * (Δl? /l + Δl? /l) )
= (F/A) / ( (1/2) * (F/ (AY? ) + F/ (AY? ) )
= 2Y? Y? / (Y? + Y? )
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