Question:

A thin 1 m long rod has a radius of 5 mm. A force of 50π kN 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?

The figure of merit is the largest for the length of the rod.

The maximum value of Y that can be determined is 10¹⁴ N/m².

ΔY/Y gets minimum contribution from the uncertainty in the length.

ΔY/Y gets its maximum contribution from the uncertainty in strain

Y = Fl/πr²Δl = (50 × π × 10³ × 1) / (π × (0.005)² × 0.01 × 10⁻³) = 2 × 10¹⁴ N/m²