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Correction for pull or tension in a tape is given as :

  • A.\(Cp = \frac{L}{AE\,(P - P_{o})}\)
  • B.\(Cp = \frac{(P - P_{o})L}{AE}\)
  • C.\(Cp = \frac{(P - P_{o})}{LAE}\)
  • D.\(Cp = \frac{(P - P_{o})AE}{L}\)

Answer: B

The pull correction is \(Cp = \frac{(P - P_{o})L}{AE}\).

A tape is standardised under a pull \(P_o\). If it is used under a larger pull \(P\), the extra force stretches it, and by Hooke's law the extension of a length \(L\) of cross-section \(A\) and modulus \(E\) is:

\[ C_p = \frac{(P - P_o)\,L}{A\,E} \]

The correction is positive when \(P > P_o\). The other options misplace terms: an extension must grow with both the excess pull and the length, so neither can sit in the denominator, and \(AE\) is the stiffness that resists stretching, so it cannot be in the numerator.

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