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A smooth uniform string of natural lengt...

A smooth uniform string of natural length `L_0`, cross-sectional area `A` and Young's modulus `Y` is pulled along its length by a force `F` on a horizontal smooth surface. The elastic potential energy stored in the string is

A

`U =m (F^(2) l)/(AY)`

B

`U = (F^(2) l)/(3AY)`

C

`U = (F^(2)l)/(6AY)`

D

`U = (F^(2) l)/(2AY)`

Text Solution

Verified by Experts

The correct Answer is:
C
As discueed earlier, the tension `T` in the string at a distance `x` from its end is given as:
`T = (F)/(l) x,` Hence, `p = (T)/(A) = (F)/(Al)x`
substituing `(p)` in the , Hence, `p = (T)/(A) = (F)/(AL)x`
substituiting `(p)` in the formula `U = (1)/(2Y) int p^(2) dv`
we have, `U = (1)/(2Y) int_(0)^(1) (F^(2))/(A^(2) l^(2)) x^(2) dv`,
where `dv = Adx` This gives `U = (F^(2)l)/(6AY)`
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