Q

# How to solve this problem- - Properties of Solids and Liquids - JEE Main-2

At $40^{\circ}C$, a brass wire of 1 mn 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 ; $g=10ms^{-2}$)

• Option 1)

$9kg$

• Option 2)

$0.9kg$

• Option 3)

$1.5kg$

• Option 4)

$0.5kg$

Views

$Mg=\left ( \frac{Ay}{l} \right )\triangle l$

also we know $\Rightarrow \frac{\triangle l}{l} = \alpha \triangle T$

$\Rightarrow Mg=Ay \alpha \triangle T$

$\Rightarrow M= \frac{Ay\alpha\triangle T}{g}=6.28$

As $6.28$ is closet to $9$

hence option (1) is correct

Option 1)

$9kg$

Option 2)

$0.9kg$

Option 3)

$1.5kg$

Option 4)

$0.5kg$

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