A compressive force, $F$ is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by $\Delta T$. The net change in its length is zero. Let $l$ be the length of the rod, $A$ its area of cross- section, $Y$ its Young's modulus, and $\alpha $ its coefficient of linear expansion. Then, $F$ is equal to
A compressive force, $F$ is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by $\Delta T$. The net change in its length is zero. Let $l$ be the length of the rod, $A$ its area of cross- section, $Y$ its Young's modulus, and $\alpha $ its coefficient of linear expansion. Then, $F$ is equal to
- [JEE MAIN 2017]
- A
${l^2}\,Y\alpha \Delta T$
- B
$lA\,Y\alpha \Delta T$
- C
$A\,Y\alpha \Delta T$
- D
$\frac{{AY}}{{\alpha \Delta T}}$
Similar Questions
The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied ?
The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied ?
Increase in length of a wire is $1\, mm$ when suspended by a weight. If the same weight is suspended on a wire of double its length and double its radius, the increase in length will be ........ $mm$
Increase in length of a wire is $1\, mm$ when suspended by a weight. If the same weight is suspended on a wire of double its length and double its radius, the increase in length will be ........ $mm$
A steel rod of length $1\,m$ and cross sectional area $10^{-4}\,m ^2$ is heated from $0^{\circ}\,C$ to $200^{\circ}\,C$ without being allowed to extend or bend. The compressive tension produced in the rod is $........\times 10^4\,N$ (Given Young's modulus of steel $=2 \times 10^{11}\,Nm ^{-2}$, coefficient of linear expansion $=10^{-5}\, K ^{-1}$.
A steel rod of length $1\,m$ and cross sectional area $10^{-4}\,m ^2$ is heated from $0^{\circ}\,C$ to $200^{\circ}\,C$ without being allowed to extend or bend. The compressive tension produced in the rod is $........\times 10^4\,N$ (Given Young's modulus of steel $=2 \times 10^{11}\,Nm ^{-2}$, coefficient of linear expansion $=10^{-5}\, K ^{-1}$.
- [JEE MAIN 2023]
The value of Young's modulus for a perfectly rigid body is ...........
The value of Young's modulus for a perfectly rigid body is ...........
Two identical solid balls, one of ivory and the other of wet-clay are dropped from the same height on the floor. Which one will rise to a greater height after striking the floor and why ?
Two identical solid balls, one of ivory and the other of wet-clay are dropped from the same height on the floor. Which one will rise to a greater height after striking the floor and why ?