At 40,^oC , a brass wire of 1, mm is hung from ceiling. A small mass, M is hung from free end of wir

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10-1.Thermometry, Thermal Expansion and Calorimetry

hard

At $40\,^oC$, a brass wire of $1\, mm$ is hung from the ceiling. A small mass, $M$ is hung from the free end of the wire. When the wire is cooled down from $40\,^oC$ to $20\,^oC$ it regains its original length of $0.2\, m$. The value of $M$ is close to ........$kg$ (Coefficient of linear expansion and Young's modulus of brass are $10^{-5}/^oC$ and $10^{11}\, N/m^2$, respectively; $g = 10\, ms^{-2}$)

A

$0.5$

B

$9$

C

$0.9$

D

$1.5$

(JEE MAIN-2019)

Solution

$\begin{array}{l}
Mg = \left( {\frac{{Ay}}{l}} \right)\,\Delta l\\
Mg = \left( {Ay} \right)\,\alpha \Delta T = 2\pi
\end{array}$

It is closest to $9$

Standard 11

Physics

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