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  • A thin 1 m long rod has a radius of 5 mm. A force of 50 π k N is applied at one end to determine its Young’s modulus.   Assume that the force is exactly known.  If

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

 

Option: 1

       \frac{\Delta Y}{Y}   gets minimum contribution from the uncertainty in the length.


Option: 2

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


Option: 3

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


Option: 4

\frac{\Delta Y}{Y} gets its maximum contribution from the uncertainty in strain


Answers (1)

best_answer

\begin{aligned} &\text { Here } L=1 m, r=5 m m=5 \times 10^{-3} m\\ &F=50 \pi k N \text { L.C of all lengths }=0.01 m m\\ &Y=?\\ &Y=\frac{\text {strees}}{\text {sta} \in}=\frac{F L}{A l}=\frac{F L}{\pi r^{2} l}\\ &Y=\frac{50 \pi \times 10^{3}}{\pi\left(5 \times 10^{-3}\right)^{2}} \times \frac{L}{l}=2 \times 10^{9} \times \frac{L}{l}=\frac{2 \times 10^{9}}{l}\\ &\frac{\Delta Y}{Y}=2 \frac{\Delta r}{r}+\frac{\Delta L}{L}+\frac{\Delta l}{l} \end{aligned}

 

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Ritika Kankaria

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