A force is applied to a steel wire 'A',rigidl | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The Young's modulus $Y$ is given by $Y = \frac{F/A}{\Delta \ell / \ell}$,where $F$ is the force,$A$ is the cross-sectional area,$\ell$ is the orig

Vedclass · Accepted Answer

$6.9$

Vedclass · Answer

(D) The Young's modulus $Y$ is given by $Y = \frac{F/A}{\Delta \ell / \ell}$,where $F$ is the force,$A$ is the cross-sectional area,$\ell$ is the original length,and $\Delta \ell$ is the elongation.Since the material is the same (steel),$Y$ is constant. Rearranging the formula,we get $\Delta \ell = \frac{F \ell}{Y A}$.For wire '$A$': $\Delta \ell_A = \frac{F \ell_A}{Y A_A} = 0.2\,mm$.For wire '$B$': $\ell_B = 2 \ell_A$ and $d_B = 2.4 d_A$. Since $A = \pi (d/2)^2$,the area $A_B = (2.4)^2 A_A = 5.76 A_A$.Now,$\Delta \ell_B = \frac{F \ell_B}{Y A_B} = \frac{F (2 \ell_A)}{Y (5.76 A_A)} = \frac{2}{5.76} 	imes \left( \frac{F \ell_A}{Y A_A} ight)$.Substituting $\Delta \ell_A = 0.2\,mm$: $\Delta \ell_B = \frac{2}{5.76} 	imes 0.2 = \frac{0.4}{5.76} \approx 0.06944\,mm$.Converting to the required format: $0.06944\,mm = 6.944 	imes 10^{-2}\,mm$. Rounding to the nearest option,we get $6.9 	imes 10^{-2}\,mm$.

Similar Questions

$A$ $100\,m$ long wire having cross-sectional area $6.25 \times 10^{-4}\,m^2$ and Young's modulus $10^{10}\,N/m^2$ is subjected to a load of $250\,N$. The elongation in the wire will be:

Three bars having lengths $l, 2l$,and $3l$ and areas of cross-section $A, 2A$,and $3A$ are joined rigidly end to end. The compound rod is subjected to a stretching force $F$. The total increase in the length of the rod is (Young's modulus of the material is $Y$ and the bars are massless).

The unit of Young's modulus is

What is the velocity of sound in a perfectly rigid rod? Why?

$A$ wire of cross-sectional area $10^{-6} \, m^2$ is elongated by $0.1 \%$ when the tension in it is $1000 \, N$. The Young's modulus of the material of the wire is (Assume radius of the wire is constant).

Vedclass Test Series

Exam Paper Generator

Online Exam Module