Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Medical
  • A uniform wire ( Young's modulus  ) is subjected to longitud

A uniform wire ( Young's modulus 2\times 10^{11}Nm^{-2} ) is subjected to longitudinal tensile stress of 5\times 10^{7}Nm^{-2}. If the overall volume change in the wire is 0.02%, the fractional decrease in the radius of the wire is close to : 

Option: 1

1.0\times 10^{-4}
 


Option: 2

1.5\times 10^{-4}


Option: 3

0.25\times 10^{-4}

 


Option: 4

5\times 10^{-4}


Answers (1)

best_answer

\begin{aligned} &Y=\frac{\text {Stress}}{\Delta L / L}\\ &\frac{\Delta L}{L}=\frac{\text {stress}}{Y}=\frac{5 \times 10^{7}}{2 \times 10^{11}}=2.5 \times 10^{-4}\\ &\text { Now } V=\pi r^{2} L\\ &\frac{\Delta V}{V}=\frac{\pi \Delta\left(r^{2} L\right)}{\pi r^{2} L}=\frac{r^{2} \Delta L+L \times 2 r \Delta r}{r^{2} L} \end{aligned}

\begin{aligned} &\frac{\Delta L}{L}+2 \frac{\Delta r}{r}\\ &2 \frac{\Delta r}{r}=\frac{\Delta V}{V}-\frac{\Delta L}{L}=\frac{0.02}{100}-2.5 \times 10^{-4}\\ &\frac{\Delta r}{r}=1 \times 10^{-4}-\frac{2.5}{2} \times 10^{-4}=-0.25 \times 10^{-4} \end{aligned}

Posted by

himanshu.meshram

View full answer

NEET 2024 Most scoring concepts

    Just Study 32% of the NEET syllabus and Score up to 100% marks

Similar Questions

Trending Articles/News

anam-khan

NEET UG 2026 LIVE: NTA to start registrations at neet.nta.nic.in shortly; 1.29 lakh MBBS seats
anam-khan

Rabri Devi accuses Bihar govt of 'covering up' facts in NEET aspirant death case
anam-khan

NEET UG 2026 Registration LIVE: NTA to begin NEET form soon at neet.nta.nic.in; exam date, fees updates

Latest Question