Question

A thick copper rope of density $1.5 \times 10^{3} kg / m ^{3}$ and young's modulus $5 \times 10^{6} N / m ^{2}, 8 \,m$ in length is hung from the ceiling of a room. The increase in its length due to its own weight is

• A. $9.6 \times 10^{-5} \,m$
• B. $9.6 \times 10^{-7} \,m$
• C. $19.2 \times 10^{-7} \,m$
• D. $9.6 \times 10^{-2} m$

Answer 1

Answer: (D)

The increase in length due to its own weight $l=\frac{L^{2} d g}{2 Y}$
$=\frac{(8)^{2} \times 1.5 \times 10^{3} \times 9.8}{2 \times 5 \times 10^{6}}$
$=9.6 \times 10^{-2} m$