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

Consider the following reaction:
$C_6H_5COCl \xrightarrow{H_2, Pd-BaSO_4} 'A'$
The product $'A'$ is:

$A$ variable plane passes through a fixed point $(1, 2, 3)$. The foot of the perpendicular from the origin to the plane lies on:

The reading of the ammeter in the circuit shown will be: (in $A$)

$A$ metal rod moves at a constant velocity in a direction perpendicular to its length. $A$ constant uniform magnetic field exists in space in a direction perpendicular to the rod as well as its velocity. Select the correct statement from the following:

Chemical $A$ is used for the removal of temporary hardness of water. Compound $A$ reacts with $Na_2CO_3$ to produce caustic soda. When $CO_2$ gas is passed through $A$,it turns milky. What is the chemical formula of $A$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module