A thin rod having a length of $1\; m$ and area of cross-section $3 \times 10^{-6}\,m ^2$ is suspended vertically from one end. The rod is cooled from $210^{\circ}\,C$ to $160^{\circ}\,C$. After cooling, a mass $M$ is attached at the lower end of the rod such that the length of rod again becomes $1\,m$. Young's modulus and coefficient of linear expansion of the rod are $2 \times 10^{11} Nm ^{-2}$ and $2 \times 10^{-5} K ^{-1}$, respectively. The value of $M$ is $.......kg .\left(\right.$ Take $\left.g=10\,m s ^{-2}\right)$
A thin rod having a length of $1\; m$ and area of cross-section $3 \times 10^{-6}\,m ^2$ is suspended vertically from one end. The rod is cooled from $210^{\circ}\,C$ to $160^{\circ}\,C$. After cooling, a mass $M$ is attached at the lower end of the rod such that the length of rod again becomes $1\,m$. Young's modulus and coefficient of linear expansion of the rod are $2 \times 10^{11} Nm ^{-2}$ and $2 \times 10^{-5} K ^{-1}$, respectively. The value of $M$ is $.......kg .\left(\right.$ Take $\left.g=10\,m s ^{-2}\right)$
- [JEE MAIN 2023]
- A
$60$
- B
$59$
- C
$58$
- D
$57$
Similar Questions
A bimetallic strip consists of metals $A$ and $B$. It is mounted rigidly as shown. The metal $A$ has higher coefficient of expansion compared to that of metal $B$. When the bimetallic strip is placed in a cold both, it will :
A bimetallic strip consists of metals $A$ and $B$. It is mounted rigidly as shown. The metal $A$ has higher coefficient of expansion compared to that of metal $B$. When the bimetallic strip is placed in a cold both, it will :
- [JEE MAIN 2021]
A student records the initial length $l$, change in temperature $\Delta T$ and change in length $\Delta l$ of a rod as follows :
S.No.
$l(m)$
$\Delta T{(^o}C)$
$\Delta l(m)$
$(1)$
$2$
$10$
$4\times 10^{-4}$
$(2)$
$1$
$10$
$4\times 10^{-4}$
$(3)$
$2$
$20$
$2\times 10^{-4}$
$(4)$
$3$
$10$
$6\times 10^{-4}$
If the first observation is correct, what can you say about observations $2,\,3$ and $4$.
A student records the initial length $l$, change in temperature $\Delta T$ and change in length $\Delta l$ of a rod as follows :
| S.No. | $l(m)$ | $\Delta T{(^o}C)$ | $\Delta l(m)$ |
| $(1)$ | $2$ | $10$ | $4\times 10^{-4}$ |
| $(2)$ | $1$ | $10$ | $4\times 10^{-4}$ |
| $(3)$ | $2$ | $20$ | $2\times 10^{-4}$ |
| $(4)$ | $3$ | $10$ | $6\times 10^{-4}$ |
If the first observation is correct, what can you say about observations $2,\,3$ and $4$.
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A uniform cylindrical rod of length $L$ and radius $r$, is made from a material whose Young's modulus of Elasticity equals $Y$. When this rod is heated by temperature $T$ and simultaneously subjected to a net longitudinal compressional force $F$, its length remains unchanged. The coefficient of volume expansion, of the material of the rod, is (nearly) equals to
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