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A wire is length 2l, radius r and Young'...

A wire is length `2l`, radius `r` and Young's modulus `Y` pulled perpendicular to its mid point by a distance `y`. Fina the tesnion in the wire

A

`= (pi r^(2) y^(2) Y)/(l^(2))`

B

`= (pi r^(2) y^(2) Y)/(2l^(2))`

C

`= (r^(2) y^(2) Y)/(2l^(2))`

D

`= (r^(2) y^(2) Y)/(l^(2))`

Text Solution

Verified by Experts

The correct Answer is:
B
The increases in length of the wire is
`Delta l = 2 (sqrt(l^(2) + y^(2))-l) = 2l [(1 + (y^(2))/(l^(2)))^(1//2) - 1]`
`2l (y^(2))/(2l^(2)) = (y^(2))/(l) ( :. y lt lt l)`
Then, strian `= e = (Delta l)/(2l) = (y^(2))/(2l^(2)),` since `(F)/(A) = eY`
we have `F = eYA = [(y^(2))/(2l^(2))] (pi r^(2)) (Y), = (pi r^(2) y^(2) Y)/(2l^(2))`
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