A metal rod of Young's modulus 2 × 1010 Nm -2 undergoes an elastic strain of 0.06 % . The energy per unit volume stored in Jm -3 is

Question

A metal rod of Young's modulus 2 × 1010 Nm -2 undergoes an elastic strain of 0.06 % . The energy per unit volume stored in Jm -3 is (A) 3600 (B) 7200 (C) 10800 (D) 14400

Tardigrade Admin · Accepted Answer

Energy density =(1/2) × stress × strain =(1/2)(Y × strain ) × strain =(1/2)(2 × 1010 Nm -2)((0.06/100))2 =3600 Jm -3

Q. A metal rod of Young's modulus $2 \times 1 0^{10} N m^{- 2}$ undergoes an elastic strain of $0.06%.$ The energy per unit volume stored in $J m^{- 3}$ is

3600

7200

10800

14400

Energy density $= \frac{1}{2} \times$ stress $\times$ strain
$= \frac{1}{2} (Y \times$ strain $) \times$ strain
$= \frac{1}{2} (2 \times 1 0^{10} N m^{- 2}) (\frac{0.06}{100})^{2}$
$= 3600 J m^{- 3}$

Q. A metal rod of Young's modulus 2×1010Nm−2 undergoes an elastic strain of 0.06%. The energy per unit volume stored in Jm−3 is