In the given figure, if the dimensions of the two wires are same but materials are different, then Young's modulus is $ ........$
Medium
Download our app for free and get started
At same value of load
$A$ has less elongation than $B \ldots (1)$
$\frac{F L}{A Y}=\Delta L$ $\left\{\begin{array}{l}\because L, A \text { are same } \\ F \text { - Load is also taken same }\end{array}\right\}$
So $\frac{1}{Y} \propto \Delta L \ldots (2)$
Using conditions $(1)$ and $(2)$
We can say
$Y_A > Y_B$ $\{$ Young's modulus of $A$ greater than $B\}$
$A$ has less elongation than $B \ldots (1)$
$\frac{F L}{A Y}=\Delta L$ $\left\{\begin{array}{l}\because L, A \text { are same } \\ F \text { - Load is also taken same }\end{array}\right\}$
So $\frac{1}{Y} \propto \Delta L \ldots (2)$
Using conditions $(1)$ and $(2)$
We can say
$Y_A > Y_B$ $\{$ Young's modulus of $A$ greater than $B\}$
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
- 1A force is applied to a steel wire ' $A$ ', rigidly clamped at one end. As a result elongation in the wire is $0.2\,mm$. If same force is applied to another steel wire ' $B$ ' of double the length and a diameter $2.4$ times that of the wire ' $A$ ', the elongation in the wire ' $B$ ' will be $............\times 10^{-2}\,mm$ (wires having uniform circular cross sections)View Solution
- 2A rubber ball is taken to a $100\, m$ deep lake and its volume changes by $0.1\%$. The bulk modulus of rubber is nearlyView Solution
- 3A $5\, m$ long aluminium wire ($Y = 7 \times {10^{10}}N/{m^2})$ of diameter $3\, mm$ supports a $40\, kg$ mass. In order to have the same elongation in a copper wire $(Y = 12 \times {10^{10}}N/{m^2})$ of the same length under the same weight, the diameter should now be, in $mm.$View Solution
- 4Two blocks of masses $m$ and $M$ are connected by means of a metal wire of cross-sectional area $A$ passing over a frictionless fixed pulley as shown in the figure. The system is then released. If $M = 2\, m$, then the stress produced in the wire isView Solution
- 5Two wires $A$ and $B$ are of same materials. Their lengths are in the ratio $1 : 2$ and diameters are in the ratio $2 : 1$ when stretched by force ${F_A}$ and ${F_B}$ respectively they get equal increase in their lengths. Then the ratio ${F_A}/{F_B}$ should beView Solution
- 6A force $F$ is applied on a square area of side $L$. If the percentage error in the measurement of $L$ is $2 \%$ and that in $F$ is $4 \%$, what is the maximum percentage error in pressure?View Solution
- 7Two blocks of masses $3 \,{kg}$ and $5\, {kg}$ are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is $\frac{24}{\pi} \times 10^{2}\, {Nm}^{-2}$. What is the minimum radius of the wire? (Take $\left.g=10\, {ms}^{-2}\right)$ (in $cm$)View Solution
- 8The proportional limit of steel is $8 \times 10^8 \,N / m ^2$ and its Young's modulus is $2 \times 10^{11} \,N / m ^2$. The maximum elongation, a one metre long steel wire can be given without exceeding the elastic limit is ...... $mm$View Solution
- 9A vertical hanging bar of length $l$ and mass $m$ per unit length carries a load of mass $M$ at lower end, its upper end is clamped to a rigid support. The tensile stress a distance $x$ from support is $(A \rightarrow$ area of cross-section of bar)View Solution
- 10A steel rod of length $\ell$, cross sectional area $A$, young's modulus of elasticity $Y$, and thermal coefficient of linear expansion $'a'$ is heated so that its temperature increases by $t\,^oC$. Work that can be done by rod on heating will beView Solution