The Young's modulus (Y) of the material of a wire is given by `Y=(MgL)/(pir^(2)l)`.
The percentage errors in the load (Mg) suspended at the lower end, original length (L), radius (r ) and the extension (l) are 1%, 1.5%, 2% and 2.5% respectively. What is the maximum possible percentage error in Y?
[Take `g=10m//s^(2)`]

Options

A. `5.5%`
B. `7.5%`
C. `9%`
D. `11%`

Answer

c

Explanation

`Y=(MgL)/(pir^(2)l)`
[In this case, the values of g and `pi` are constant. As they are not measured, they are not considered in the calculations of errors.]
`therefore` From the above equation, the maximum possible percentage error is given by
`(DeltaY)/(Y)xx100=((DeltaM)/(M)+(DeltaL)/(L)+2(Deltar)/(r)+(Deltal)/(l))xx100`
[We have to add the errors in quantities involved in multiplication as well as in division.
`therefore (DeltaY)/(Y)=1%+1.5%+2xx2%+2.5%=9%`