$A$ rod of length $1000\, mm$ and coefficient of linear expansion $a = 10^{-4}$ per degree is placed symmetrically between fixed walls separated by $1001\, mm$. The Young’s modulus of the rod is $10^{11} N/m^2$. If the temperature is increased by $20^o C$, then the stress developed in the rod is ........... $MPa$
Diffcult
Download our app for free and get started
$\Delta \ell=\ell \alpha \Delta T=2 m m$
$\Delta \ell_{\text {actual }}=2-1=1 \mathrm{mm}$
$\sigma=\mathrm{Y}\left(\frac{\Delta \ell_{\mathrm{actual}}}{\ell}\right)$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1When load of $5\,kg$ is hung on a wire then extension of $3\,m$ takes place, then work done will be ....... $joule$View Solution
- 2A wire is loaded by $6\, kg$ at its one end, the increase in length is $12\, mm.$ If the radius of the wire is doubled and all other magnitudes are unchanged, then increase in length will be ......... $mm$View Solution
- 3A copper wire of length $1.0\, m$ and a steel wire of length $0.5\, m$ having equal cross-sectional areas are joined end to end. The composite wire is stretched by a certain load which stretches the copper wire by $1\, mm$. If the Young's modulii of copper and steel are respectively $1.0\times10^{11}\, Nm^{-2}$ and $2.0\times10^{11}\, Nm^{- 2}$, the total extension of the composite wire is ........ $mm$View Solution
- 4In plotting stress versus strain curves for two materials $P$ and $Q$, a student by mistake puts strain on the $y$-axis and stress on the $x$-axis as shown in the figure. Then the correct statement$(s)$ is(are)View Solution
$(A)$ $P$ has more tensile strength than $Q$
$(B)$ $P$ is more ductile than $Q$
$(C)$ $P$ is more brittle than $Q$
$(D)$ The Young's modulus of $P$ is more than that of $Q$
- 5Match List-$I$ with List-$II$ :View Solution
List-$I$ List-$II$ $(A)$ A force thatrestores anelastic body of unit area to its original state $(I)$ Bulkmodulus $(B)$ Two equal andopposite forcesparallel toopposite faces $(II)$Young'smodulus $(C)$Forcesperpendiculareverywhere tothe surface perunit areasameeverywhere $(III)$ Stress $(D)$Two equal andopposite forceperpendicular toopposite faces $(IV)$ Shearmodulus Choose the correct answer from the options given below:
- 6View SolutionDue to addition of impurities, the modulus of elasticity
- 7Young's modules of material of a wire of length ' $L$ ' and cross-sectional area $A$ is $Y$. If the length of the wire is doubled and cross-sectional area is halved then Young's $modules$ will be :View Solution
- 8View SolutionOn stretching a wire, the elastic energy stored per unit volume is
- 9A wire $2 \,m$ in length suspended vertically stretches by $10 \,mm$ when mass of $10 \,kg$ is attached to the lower end. The elastic potential energy gain by the wire is $...... J ($take $g=10 \,m / s ^2 )$View Solution
- 10When a certain weight is suspended from a long uniform wire, its length increases by one $cm$. If the same weight is suspended from another wire of the same material and length but having a diameter half of the first one, the increase in length will be ......... $cm$View Solution