The temperature of a wire of length 1 , m and | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The thermal stress developed in a rod when its expansion is prevented is given by $\sigma = Y \alpha \Delta 	heta$.Since stress $\sigma = F/A$,th

Vedclass · Accepted Answer

$10^4 \, N$

Vedclass · Answer

(B) The thermal stress developed in a rod when its expansion is prevented is given by $\sigma = Y \alpha \Delta 	heta$.Since stress $\sigma = F/A$,the force $F$ is given by $F = Y A \alpha \Delta 	heta$.Given:$Y = 10^{11} \, N/m^2$$A = 1 \, cm^2 = 10^{-4} \, m^2$$\alpha = 10^{-5} /^\circ C$$\Delta 	heta = 100 - 0 = 100^\circ C = 10^2 \, ^\circ C$Substituting these values into the formula:$F = 10^{11} 	imes 10^{-4} 	imes 10^{-5} 	imes 10^2$$F = 10^{11 - 4 - 5 + 2} = 10^4 \, N$.

The temperature of a wire of length $1 \, m$ and area of cross-section $1 \, cm^2$ is increased from $0^\circ C$ to $100^\circ C$. If the rod is not allowed to increase in length,the force required will be $(\alpha = 10^{-5} /^\circ C$ and $Y = 10^{11} \, N/m^2)$.

Similar Questions

The volume of a metal sphere increases by $0.15\%$ when its temperature is raised by $24\,^{\circ}C$. The coefficient of linear expansion of the metal is:

The coefficient of superficial expansion of a solid is $2 \times 10^{-5} \text{ °C}^{-1}$. Its coefficient of linear expansion is:

$A$ steel tape gives correct measurement at $20^{\circ} C$. $A$ piece of wood is being measured with the steel tape at $0^{\circ} C$. The reading is $25 \ cm$ on the tape. The real length of the given piece of wood must be:

Solids expand on heating because ................

$A$ cylindrical metal rod of length $L_0$ is shaped into a ring with a small gap $x$ as shown. On heating the system:

Vedclass Test Series

Exam Paper Generator

Online Exam Module