A thin `1m` long rod has a radius of `5mm`. A force of `50pi 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 `0.01mm` which of the following statements is false ?

Options

A. The maximum value of `Y` that can be determined is `10^(14)N//m^(2)`
B. `(DeltaY)/(Y)` gets minimum contribution from the unicertainity in the length
C. `(DeltaY)/(Y)` gets minimum contribution from the unicertainity in strain
D. The figure of merit is the largest for the length of the rod

Answer

A

Explanation

Here `L=1m`, `r=5mm=5xx10^(-3)m`
`F=50pikN` L.C of all lengths `=0.01mm`
`Y=?`
`Y=(strees)/(stain)=(FL)/(Al)=(FL)/(pir^(2)l)`
`Y=(50pixx10^(3))/(pi(5xx10^(-3))^(2))xx(L)/(l)=2xx10^(9)xx(L)/(l)=(2xx10^(9))/(l)`
`(DeltaY)/(Y)=2(Deltar)/(r)+(DeltaL)/(L)+(Deltal)/(l)`