A uniform cylindrical rod of length L and rad | vedclass

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

Question

(C) The length of the cylinder remains unchanged,which means the thermal expansion is exactly compensated by the longitudinal compression.The thermal

Vedclass · Accepted Answer

$3F / (\pi r^2 YT)$

Vedclass · Answer

(C) The length of the cylinder remains unchanged,which means the thermal expansion is exactly compensated by the longitudinal compression.The thermal expansion strain is given by $\Delta L / L = \alpha T$,where $\alpha$ is the coefficient of linear expansion.The compressive strain due to force $F$ is given by $\Delta L / L = 	ext{Stress} / Y = F / (A Y) = F / (\pi r^2 Y)$.Equating the two strains: $\alpha T = F / (\pi r^2 Y)$.Therefore,$\alpha = F / (\pi r^2 YT)$.The coefficient of volume expansion $\gamma$ is related to the coefficient of linear expansion $\alpha$ by the relation $\gamma = 3\alpha$.Substituting the value of $\alpha$,we get $\gamma = 3F / (\pi r^2 YT)$.

Similar Questions

$A$ steel rod of diameter $1\,cm$ is clamped firmly at each end when its temperature is $25\,^{\circ}C$ so that it cannot contract on cooling. The tension in the rod at $0\,^{\circ}C$ is approximately ......... $N$ $(\alpha = 10^{-5}/\,^{\circ}C, Y = 2 \times 10^{11}\,N/m^2)$

There are two wires of the same material and same length. If the diameter of the second wire is two times the diameter of the first wire,then the ratio of the extension produced in the wires by applying the same load will be:

Two steel wires of same length $L$ but radii $r$ and $2r$ are connected together end to end and tied to a wall as shown. The force $F$ stretches the combination by $10 \ mm$. How far does the junction point $A$ move (in $mm$)?

$A$ wire of length $2L$ is fixed between two walls. When a weight $W = mg$ is applied at its midpoint,it sags by a distance $x$ $(x << L)$. Then $m$ is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module