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  4. At 40°C, a brass wire of 1 mm radius 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°C to 20°C it regains its original length of 0.2 m. The value of M is close to: (Coefficient of linear expansion and Young's modulus of brass are 10-5/°C and 1011 N/m2, respectively; g = 10 ms-2)

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Q. At $40^{\circ}C$, a brass wire of $1\, mm$ radius 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 $40^{\circ}C$ to $20^{\circ}C$ it regains its original length of $0.2\, m$. The value of $M$ is close to :
(Coefficient of linear expansion and Young's modulus of brass are $10^{-5}/{^{\circ}}C$ and $10^{11} \; N/m^2$, respectively; $g = 10\, ms^{-2}$)

JEE MainJEE Main 2019Thermal Properties of Matter

Solution:

$Mg =\left(\frac{Ay}{\ell}\right)\Delta\ell $
$ \frac{\Delta\ell}{\ell} =\alpha\Delta T $
$ Mg = \left(Ay\right)\alpha\Delta T = 2\pi $
It is closest to $9$.