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A thin 1 m long rod has a radius of 5 mm . A force of 50 π×10 3 N is applied at one end to determine its Young's modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is 0 . 01 mm , which of the following statements is false?

Options

  1. AThe maximum value of Y that can be determined is 2 × 10 14   N   m - 2
  2. B∆ Y Y gets minimum contribution from the uncertainty in the length.
  3. C∆ Y Y gets its maximum contribution from the uncertainty in strain.
  4. DThe figure of merit is the largest for the length of the rod.

Correct answer

A. The maximum value of Y that can be determined is 2 × 10 14   N   m - 2

Step-by-step solution

Given, l = 1   m , r = 5 × 1 0 - 3   m and F = 5 0 π × 1 0 3   N . Least count in length is = 0 . 01   mm = 0.01 × 10 - 3   m Young's modulus is given by Y = F A ∆ l l For, ∆ l → Min , Y → Max ⇒ Y Δ l l = F A Y = 5 0 π × 1 0 3 π × 5 × 1 0 - 3 2 × l Δ l Y = 5 0 × 1 0 3 2 5 × 1 0 - 6 × 1 Δ l ⇒ Y = 2 × 1 0 9 Δ l Here Δ l is unknown so we can not find the Y The

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