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A wire of length L and area of cross-sec...

A wire of length L and area of cross-section A, is stretched by a load. The elongation produced in the wire is I. If Y is the Young's modulus of the material of the wire, then the force costant of the wire is

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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