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

The elongation of the copper wire of cross-sectional area $3.5 \,mm^2$, as shown in the figure, is (Given: $Y_{\text{copper}} = 10 \times 10^{10} \,N/m^2$ and $g = 10 \,m/s^2$).

When a force of $4 \, N$ is applied to a wire,its length is $a \, m$. When a force of $5 \, N$ is applied,its length is $b \, m$. What will be its length when a force of $9 \, N$ is applied?

Let $L$ be the length and $d$ be the diameter of the cross-section of a wire. Wires of the same material with different $L$ and $d$ are subjected to the same tension along the length of the wire. In which of the following cases will the extension of the wire be the maximum?

The following four wires are made of the same material. Which one will have the largest elongation when subjected to the same tension?

Two wires of the same length and same cross-sectional area are suspended as shown in the figure. Their Young's moduli are $Y_1$ and $Y_2$. What is their equivalent Young's modulus?

Vedclass Test Series

Exam Paper Generator

Online Exam Module