Question

A wire of length $1\text{m}$, area of cross section $2{\text{mm}}^2$ is hanging from a ceiling of lift. The length of the wire changes to $1.1\text{m}$ when a mass $2\text{kg}$ is suspended from its free end and lift is accelerated upwards with acceleration $2{\text{m/s}}^2$. The value of Young’s modulus is

$(g=10{\text{m/s}}^2)$

• A. $4.2\times {10}^4{\text{N/m}}^2$
• B. $6\times {10}^4{\text{N/m}}^2$
• C. $1.2\times {10}^8{\text{N/m}}^2$
• D. $8\times {10}^3{\text{N/m}}^2$

Answer 1

The correct option is C $1.2\times {10}^8{\text{N/m}}^2$


From the definition of Young’s modulus

$Y=\frac{\text{stress}}{\text{strain}}$

$Y=\frac{TL}{A\Delta L}$

Here, $T=M(g+a)$

$\Rightarrow Y=\frac{M(g+a)L}{A(L_1-L)}=\frac{2(10+2)\times 1}{2\times {10}^{-6}\left(0.1\right)}=120\times {10}^6$

$=1.2\times {10}^8{\text{N/m}}^2$