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When a long wire is stretched by 0.25 cm...

When a long wire is stretched by 0.25 cm, the energy stored per unit volume is `0.2 Jm^(-3)`. When it is stretched by 1 cm, the increases in potential energy per unit volume sotred in the wire is given by

A

`2 J m^(-3)`

B

`3 Jm^(-3)`

C

`2.5 Jm^(-3)`

D

`4 Jm^(-3)`

Text Solution

Verified by Experts

The correct Answer is:
B
P.E./unit volume `= (1)/(2)Y("strain")^(2)`
`because (E)/(V) prop ("strain")^(2)`
`:. ((E//V)_(1))/((E//V)_(2)) = (("strain")_(1)^(2))/(("strain")_(2)^(2))`
`:. (0.2)/((E//V)_(2)) = ((0.25 xx 10^(-2))/(1 xx 10^(-2)))^(2) = (1)/(16)`
`:. (E//V)_(2) = 16 xx 0.2 = 3.2`
`:. (E//V)_(2) - (E//V)_(1) = 3.2 - 0.2 = 3 J//m^(3)`
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