The Young's modulus of the meterial of a wire is `2xx10^(10) N m^(-2)` If the elongation strain is 1% then the energy stored in the wire per unit volume is `J m^(-3) ` is

Options

A. `10^(6)`
B. `10^(8)`
C. `2 xx 10^(6)`
D. `2 xx 10^(8)`

Answer

A

Explanation

Energy stored per unit volume is `u= (1)/(2) xx` stress `xx` strain `= (1)/(2) xx Y xx "strain"^(2) = (1)/(2) Y ((Delta l)/(l))^(2)`
Here, `Y= 2 xx 10^(10) N m^(-2), (Delta l)/(l) = 1% = (1)/(100)`
`:. u= (1)/(2) xx 2 xx 10^(10) xx ((1)/(100))^(2) = 10^(6) J m^(-3)`