A metallic wire of length L is fixed between | vedclass

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

Question

(B) When the wire is cooled,it tends to contract,but since it is fixed between rigid supports,a thermal tension $F$ is developed.The thermal strain is

Vedclass · Accepted Answer

$\sqrt{\frac{Y\alpha}{\rho}}$

Vedclass · Answer

(B) When the wire is cooled,it tends to contract,but since it is fixed between rigid supports,a thermal tension $F$ is developed.The thermal strain is given by $\frac{\Delta L}{L} = \alpha \Delta T$.From Hooke's law,the tension $F$ is $F = Y A \frac{\Delta L}{L} = Y A \alpha \Delta T$,where $A$ is the cross-sectional area.The frequency of the fundamental mode of transverse vibration is $f = \frac{1}{2L} \sqrt{\frac{F}{\mu}}$,where $\mu$ is the mass per unit length.Since $\mu = \rho A$,we substitute $F$ and $\mu$ into the frequency formula:$f = \frac{1}{2L} \sqrt{\frac{Y A \alpha \Delta T}{\rho A}} = \frac{1}{2L} \sqrt{\frac{Y \alpha \Delta T}{\rho}}$.Thus,$f \propto \sqrt{\frac{Y \alpha}{\rho}}$.

$A$ metallic wire of length $L$ is fixed between two rigid supports. If the wire is cooled through a temperature difference $\Delta T$ ($Y$ = Young's modulus,$\rho$ = density,$\alpha$ = coefficient of linear expansion),then the frequency of transverse vibration is proportional to:

Similar Questions

The acute angle between the lines $6x^2 + 11xy - 10y^2 = 0$ is

Which of the following series is $NOT$ included in the sub-class $Thalamiflorae$?

$A$ gas formed by the action of alcoholic $KOH$ on ethyl iodide,decolourises alkaline $KMnO_4$. The gas is

For a suitably chosen real constant $a$,let a function $f: R-\{-a\} \rightarrow R$ be defined by $f(x) = \frac{a-x}{a+x}$. Further,suppose that for any real number $x \neq -a$ and $f(x) \neq -a$,$(f \circ f)(x) = x$. Then $f(-\frac{1}{2})$ is equal to

If $m_1$ and $m_2$ $(m_1 > m_2)$ are the slopes of the lines represented by $5x^2 - 8xy + 3y^2 = 0$,then $m_1 : m_2$ equals

Vedclass Test Series

Exam Paper Generator

Online Exam Module