Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
121 views
in General by (113k points)
closed by
A metallic rod of length 2.5 m and cross section of 20 mm2 is elongated by a load of 500 kN. If Poisson ratio is 0.25, then the increase in volume is: (assume E = 2 × 107 N/mm2)
1. 20.00 mm3
2. 30.00 mm3
3. 31.25 mm3
4. 21.25 mm3

1 Answer

0 votes
by (115k points)
selected by
 
Best answer
Correct Answer - Option 3 : 31.25 mm3

Concept:

The volumetric strain occurred in material, ev is given by

\({{\rm{e}}_{\rm{v}}} = {\rm{\;}}\frac{{{\rm{Change\;in\;Volume\;}}\left( {{\rm{\;\Delta V}}} \right)}}{{{\rm{Original\;Volume\;}}\left( {\rm{V}} \right)}}\) OR

\({e_v} = \frac{{\left( {{\sigma _x} + \;{\sigma _y} + \;{\sigma _z}} \right)\left( {1 - 2\mu } \right)}}{E}\)

Calculation:

Given:

μ = 0.25; E = 2 × 107 N/mm2; L = 2.5 m = 2500 mm; Area = 20 mm2, Load P = 500 kN.

\({\sigma _x} = \;\frac{{Force\;in\;x\;direction\;}}{{cross\;sectional\;area}}\)

\({\sigma _x} = \;\frac{{500 \times 10^3}}{{20}}=25 \times 10^3\;N/mm^2\)

Volumetric strain:

\({e_v} = \frac{{\left( {{\sigma _x} + \;{\sigma _y} + \;{\sigma _z}} \right)\left( {1 - 2\mu } \right)}}{E}\)

\({e_v} = \frac{{\left( {{(25 \times 10^3)}\; + \;{0}\; + \;{0}} \right)\left( {1 - 2\times 0.25 } \right)}}{2\times10^7}=6.25\times10^{-4}\)

\({{\rm{e}}_{\rm{v}}} = {\rm{\;}}\frac{{{\rm{Change\;in\;Volume\;}}\left( {{\rm{\;Δ V}}} \right)}}{{{\rm{Original\;Volume\;}}\left( {\rm{V}} \right)}}\)

\({\rm{Δ }}V = V \times {e_v} = \left( {Area\;\times\;length} \right) \times 6.25 \times {10^{ - 4}}\)

\(\)\({\rm{Δ }}V = V \times {e_v} = \left( {20\;\times\;2500} \right) \times 6.25 \times {10^{ - 4}}\)

ΔV = 31.25 mm3

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...