Question

Steel wire of length ‘L’ at 40°C is suspended from the ceiling and then a mass ‘m’ is hung from its free end. The wire is cooled down from 40°C to 30°C to regain its original length ‘L’. The coefficient of linear thermal expansion of the steel is ${10}^{–5}/°C,$ Young’s modulus of steel is ${10}^{11}N/m^2$ and radius of the wire is 1 mm. Assume that L >> diameter of the wire. Then the value of ‘m; in kg is nearly.

• A.
• B. 3

Answer 1

The correct option is B 3

$\frac{\left(\frac{F}{A}\right)}{\left(\frac{\Delta l}{l}\right)}=y$

$\Rightarrow \frac{mg}{A}=y\times \frac{\Delta l}{l}$ ...(i)

After cooling

$\frac{\Delta l}{l}=\alpha \times 10$

So, $m=3kg$