Question

A uniform heavy rod of weight $10 \, kg \, ms ^{-2}$, crosssectional area $100 \, cm ^{2}$ and length $20 \, cm$ is hanging from a fixed support. Young modulus of the material of the rod is $2 \times 10^{11} \, Nm ^{-2}$. Neglecting the lateral contraction, find the elongation of rod due to its own weight.

• A. $2 \times 10^{-9} \, m$
• B. $5 \times 10^{-8} \, m$
• C. $4 \times 10^{-8} \, m$
• D. $5 \times 10^{-10} \, m$

Answer 1

Answer: (D)

We know,
$\Delta \ell=\frac{W L}{2 A Y}$
$\Delta \ell=\frac{10 \times 1}{2 \times 5} \times 100 \times 10^{-4} \times 2 \times 10^{11}$
$\Delta \ell=\frac{1}{2} \times 10^{-9}$
$=5 \times 10^{-10} \,m$