In an experiment of determine the Young's modulus of wire of a length exactly $1\; m$, the extension in the length of the wire is measured as $0.4\,mm$ with an uncertainty of $\pm 0.02\,mm$ when a load of $1\,kg$ is applied. The diameter of the wire is measured as $0.4\,mm$ with an uncertainty of $\pm 0.01\,mm$. The error in the measurement of Young's modulus $(\Delta Y)$ is found to be $x \times 10^{10}\,Nm ^{-2}$. The value of $x$ is

$\left[\right.$ Take $\left.g =10\,m / s ^{2}\right]$

  • [JEE MAIN 2022]
  • A

    $25$

  • B

    $20$

  • C

    $2$

  • D

    $8$

Similar Questions

The values of a number of quantities are used in a mathematical formula. The quantity that should be most precise and accurate in measurement is the one

The relative error in the measurement of the side of a cube is $0.027$. The relative error in the measurement of its volume is .......... 

If the length of a cylinder is $l=(4.00 \pm 0.01) cm$, radius $r =(0.250 \pm 0.001) \;cm$ and mass $m =6.25 \pm 0.01\; g$. Calculate the percentage error in determination of density.

A torque meter is calibrated to reference standards of mass, length and time each with $5 \%$ accuracy. After calibration, the measured torque with this torque meter will have net accuracy of$............\%$

  • [JEE MAIN 2022]

A physical quantity $A$ is dependent on other four physical quantities $p, q, r$ and $s$ as given below $A=\frac{\sqrt{pq}}{r^2s^3} .$ The percentage error of measurement in $p, q, r$ and $s$  $1\%,$ $3\%,\,\, 0.5\%$ and $0.33\%$ respectively, then the maximum percentage error in $A$ is .......... $\%$