Question

At $40^{\circ }C$, a brass wire of $1mm$ 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 $0.2m$. 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; $g=10m{s}^{-2}$)

• A. 1.5 kg
• B. 9 kg
• C. 0.9 kg
• D. 0.5 kg

Answer 1

Answer: (B)

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