Two rods are joined between fixed supports as shown in the figure. Condition for no change in the lengths of individual rods with the increase of temperature will be
( ${\alpha _1},\,{\alpha _2},$ = linear expansion coefficient
$A_1, A_2$ = Area of rods
$Y_1, Y_2$ = Young modulus)
Two rods are joined between fixed supports as shown in the figure. Condition for no change in the lengths of individual rods with the increase of temperature will be
( ${\alpha _1},\,{\alpha _2},$ = linear expansion coefficient
$A_1, A_2$ = Area of rods
$Y_1, Y_2$ = Young modulus)
- A
$\frac{{{A_1}}}{{{A_2}}}\, = \,\frac{{{\alpha _1}{Y_1}}}{{{\alpha _2}{Y_2}}}$
- B
$\frac{{{A_1}}}{{{A_2}}}\, = \,\frac{{{L_1}{\alpha _1}{Y_1}}}{{{L_2}{\alpha _2}{Y_2}}}$
- C
$\frac{{{A_1}}}{{{A_2}}}\, = \,\frac{{{L_2}{\alpha _2}{Y_2}}}{{{L_1}{\alpha _1}{Y_1}}}$
- D
$\frac{{{A_1}}}{{{A_2}}}\, = \,\frac{{{\alpha _2}{Y_2}}}{{{\alpha _1}{Y_1}}}$
Similar Questions
A unit scale is to be prepared whose length does not change with temperature and remains $20\,cm$, using a bimetallic strip made of brass and iron each of different length. The length of both components would change in such a way that difference between their lengths remains constant. If length of brass is $40\,cm$ and length of iron will be$...cm$
$\left(\alpha_{\text {iron }}=1.2 \times 10^{-5} K ^{-1}\right.$ and $\left.\alpha_{\text {brass }}=1.8 \times 10^{-5} K ^{-1}\right)$.
A unit scale is to be prepared whose length does not change with temperature and remains $20\,cm$, using a bimetallic strip made of brass and iron each of different length. The length of both components would change in such a way that difference between their lengths remains constant. If length of brass is $40\,cm$ and length of iron will be$...cm$
$\left(\alpha_{\text {iron }}=1.2 \times 10^{-5} K ^{-1}\right.$ and $\left.\alpha_{\text {brass }}=1.8 \times 10^{-5} K ^{-1}\right)$.
- [JEE MAIN 2022]
A steel meter scale is to be ruled so that millimeter intervals are accurate within about $5 \times 10^{-5}$ $mm$ at a certain temperature. The maximum temperature variation allowable during the ruling is .......... $^oC$ (Coefficient of linear expansion of steel $ = 10 \times {10^{ - 6}}{K^{ - 1}})$
A steel meter scale is to be ruled so that millimeter intervals are accurate within about $5 \times 10^{-5}$ $mm$ at a certain temperature. The maximum temperature variation allowable during the ruling is .......... $^oC$ (Coefficient of linear expansion of steel $ = 10 \times {10^{ - 6}}{K^{ - 1}})$
$Assertion :$ In pressure-temperature $(P-T)$ phase diagram of water, the slope of the melting curve is found to be negative.
$Reason :$ Ice contracts on melting to water.
$Assertion :$ In pressure-temperature $(P-T)$ phase diagram of water, the slope of the melting curve is found to be negative.
$Reason :$ Ice contracts on melting to water.
- [AIIMS 2005]
On what value of $\alpha _l$ depends ? Write its unit.
On what value of $\alpha _l$ depends ? Write its unit.
A cuboid $ABCDEFGH$ is anisotropic with $\alpha_x = 1 × 10^{-5} /^o C$, $\alpha_y = 2 × 10^{-5} /^o C$, $\alpha_z = 3 × 10^{-5} /^o C$. Coefficient of superficial expansion of faces can be
A cuboid $ABCDEFGH$ is anisotropic with $\alpha_x = 1 × 10^{-5} /^o C$, $\alpha_y = 2 × 10^{-5} /^o C$, $\alpha_z = 3 × 10^{-5} /^o C$. Coefficient of superficial expansion of faces can be