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?

Question

Accepted Answer

(1) The maximum value of Y that can be determined is 10¹⁴ N/m².. Idea: Y=(FL)/(π r² Δ l) is largest when the measured elongation is as small as the apparatus can resolve, Δ l=0.01 mm=1×10⁻⁵ m. F=50π×10³ N, r=5×10⁻³ m, so π r²=25π×10⁻⁶ m². Yₘₐₓ=(50π×10³×1)/(25π×10⁻⁶×1×10⁻⁵)=(50×10³)/(25×10⁻¹¹)=2×10¹⁴ N/m². The statement claims 10¹⁴, which is half of that, so (a) is the false statement.

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?

Step-by-step solution

Why the other options are wrong