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A wire of radius r stretched without ten...

A wire of radius r stretched without tension along a straight line is tightly fixed at A and B(shown in fig.). What is the tension in the wire when it is pulled in the shape ACB? Assume Young's modulus of material of the wire to be Y.

A

`(pi r^(2) Y d^(3))/(2L^(2))`

B

`(pi r^(2) Y d^(2))/(2L^(2))`

C

`(pi r^(2) Y.2L^(2))/(d^(2))`

D

`(pi r^(2) Y .2L)/(d)`

Text Solution

Verified by Experts

The correct Answer is:
B
`Y= (FL)/(A Delta L) rArr F= T= (YA Delta L)/(L)`
`Delta L= 2 sqrt(L^(2) + d^(2)) - 2L`
`(Delta L)/(L)= (2 sqrt(L^(2) + d^(2))- 2L)/(2L), T= (Y pi r^(2) (sqrt(L^(2) + d^(2))-L))/(L)`
Expanding by use of binomial theorem and neglecting higher order terms `= Y pi r^(2) [sqrt(1+ (d^(2))/(L^(2)))-1] = Y pi r^(2) [1+ (d^(2))/(2L^(2))-1]`
`= (Y pi r^(2) d^(2))/(2L^(2))`
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