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Q.

A thin 1 m long rod has a radius of 5 mm. A force of 50 πkN is applied at one end of 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? 

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a

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

b

γγ gets its maximum contribution from the uncertainty in strain. 

c

γγ gets minimum contribution from the uncertainty in the length.

d

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

answer is A.

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Detailed Solution

Given,

F=50πkN, r=5mm, L=1m

we know that Young's modulus,

Y=FLAl

substituting the values,

Y=50π×103×1π×25×10-6×l=2×109l

The Young's modulus will have a maximum value of 2×109.
The change in young's modulus ratio will then be calculated as YY=2rr+ll.

If we look at this equation, we can see that the uncertainty in length contributes the least to changes in young's modulus and the uncertainty in radius contributes the most to changes in young's modulus.

Hence the correct answer is The maximum value of γ that can be determined is 1014N/m2.

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A thin 1 m long rod has a radius of 5 mm. A force of 50 πkN is applied at one end of 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?