In the experiment to determine Young's modulus of the material of a wire under tension
used in the arrangement as shown. The percentage error in the measurement
of length is `a` in the measurement of the radius of the wire is `b` and in the
measurement of the change in length of the wire is `c`. Percentage error in the measurement
of Young's modulus for a given load is

Options

A. `a-2 b+c`
B. `a-2 b-c`
C. `a+2 b+c`
D. `a+2 b`

Answer

C

Explanation

`Y =(F)/(pi r^(2))xx(l)/(Delta l)`
Taking log of both the sides
`log Y = log F + log l - log pi - 2 log r - log Delta l`
Differentiating it, we have
`(Delta Y)/(Y)=0 +(Delta l)/(l) - 0 -(2Delta r)/(r) - (Delta l)/(Delta l)`
% error, `(Delta Y)/(Y)xx100= ((Delta l)/(l) + (2Delta r)/(r) + (Delta(Delta l))/(Delta l))xx100`
`=a + 2b + c`