Question

A metal rod of Young's modulus \(2 \times 10^{10} \mathrm{Nm}^{-2}\) undergoes an elastic strain of \(0.02 \%\) the energy per unit volume stored in the rod in jouleim \(^{3}\) is
(1) 400
(2) 800
(3) 1200
(4) 1600

Answer 1

Correct option (1) 400
Explanation:
\(\frac{E}{V}=\frac{1}{2} \times\) stress \(\times\) strain
\(\frac{E}{V}=\frac{1}{2}(y)(\operatorname{strain})^{2}\)
strain \(=\frac{0.02}{1.00}=2 \times 10^{-4}\)
\(\therefore \frac{E}{v}=\frac{1}{2} \times 2 \times 10^{16} \times 4 \times 10^{-8}\) \(=4 \times 10^{2}\)
\(\frac{E}{V}=400\) Joufe \(i \mathrm{~m}^{3}\)