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Mechanical Properties Of Fluids

Question
CBSEENPH11020578

Copper of fixed volume V is drawn into wire of length l. When this wire is subjected to a constant force F, the extension produced in the wire is increment straight l. Which of the following graphs is a straight line?

  • increment straight l space versus space 1 over straight l
  • increment straight l space versus space straight l squared
  • increment straight l space versus space 1 over straight l squared
  • increment straight l space versus space straight l

Solution

B.

increment straight l space versus space straight l squared

According to Hooke's law,
Young's Modulus is given by,
straight y space equals space fraction numerator begin display style bevelled straight F over straight A end style over denominator begin display style bevelled fraction numerator increment straight l over denominator straight l end fraction end style end fraction space equals space fraction numerator straight F space xl over denominator increment straight l space straight x space straight A end fraction     ... (i)
V = A xl = constant             ... (ii)
From equations (i) and (ii), we have
space space space straight y space equals space fraction numerator straight F space straight x space straight l space straight x space straight l over denominator increment straight l space straight x space straight V end fraction
increment straight l space equals space fraction numerator straight F over denominator straight V space straight x space straight y end fraction space straight l squared

space increment straight l space proportional to space straight l squared