Question

If the temperature of a wire of length $2m$ and area of cross section $1c{m}^2$ is increased from $0^{0}C$ to ${80}^{0}C$ and is not allowed to increase in length, then required for it is $Y={10}^{10}N/m^2$

• A. $0.008N$
• B. $1.06N$
• C. $2.4N$
• D. $3.2N$

Answer 1

The correct option is A $0.008N$

Lenght$=2m$

Cross-sectional $area=1c{m}^2=0.0001m^2$

Change in temperature$=\Delta T=80-0=80°$

Force = ?

$Y=\left({10}^{10}N/m2\right)$

$\alpha ={10}^{-10}$

$Y=\left(F/A\right)/\left(\Delta l/l\right)$

$\Rightarrow \Delta l=\left(F/YA\right)\times l₀\Rightarrow l₀\times \alpha \times \Delta T$

$F=Y\times A\times \alpha \times \Delta T$

$F=\left({10}^{1}0\right)\times \left(1/10000\right)\times {10}^{-}10\times 80$

$F=0.008N$

Hence,

option $\left(A\right)$ is correct answer.