Question

One end of steel wire is fixed to ceiling of an elevator moving up with an acceleration $2 \,ms ^{-2}$ and a load of $10\, kg$ hangs from other end. Area of cross-section of the wire is $2 \,cm ^{2}$. The longitudinal strain in the wire is (Take $g =10\, ms ^{-2}$ and $Y=2 \times 10^{11} Nm ^{-2}$ )

• A. $4 \times 10^{11}$
• B. $3 \times 10^{-6}$
• C. $8 \times 10^{-6}$
• D. $2 \times 10^{-6}$

Answer 1

Answer: (B)

Here$ T=m\left(g+a_{0}\right)=10(10+2)=120 N $
$ \therefore $ Stress $=\frac{T}{A}$
$=\frac{120}{2 \times 10^{-4}}=60 \times 10^{4} Nm ^{-2} $
and $Y =\frac{\text { stress }}{\text { strain }} $
$ \therefore \text { strain } =\frac{\text { stress }}{Y} $
$=\frac{60 \times 10^{4}}{2 \times 10^{11}}=30 \times 10^{-7}=3 \times 10^{-6} $