A mild steel wire of length 2L and crosssectional area A is stretched, well within elastic limit, horizontally between two pillars as shown in figure. A mass m is suspended from the mid point of the wire, the mid point lower by distance x. Then strain in the wire is ......

A mild steel wire of length 2L and crosssectional area A is stretched,

1.	A mild steel wire of length 2L and crosssectional area A is stretched, well within elastic limit, horizontally between two pillars as shown in figure. A mass m is suspended from the mid point of the wire, the mid point lower by distance x. Then strain in the wire is ......
Answer» `(x ^(2))/(2L ^(2))` `(x)/(L)` `(x ^(2))/(L) ` `(x ^(2))/(2L)` Solution :Increase length in WIRE, `therefore DELTA L = 2 BO - 2 BD [ because BO = OC, BD= DC]=2 (BO -BD)` `=2 [ (x ^(2) + L ^(2)) ^(1//2) - L]` `=2L [ ((x ^(2))/( L ^(2)) + 1 ) ^(1//2) -1 ]` `=2L [ (1 + (x ^(2))/( L ^(2))) ^(1//2) -1 ]` `=2L [(1 + (1)/(2) (x ^(2))/( L ^(2)) + ...)-1 ] [because x lt lt L] ` By binomial theorem UPTO two terms, `= 2L xx 1/2 (x^(2))/( L ^(2))` `Delta L = (x ^(2))/( L )` `therefore` Strain `= (Delta L )/( 2L ) = (x ^(2) // L )/( 2 L ) = (x ^(2))/( 2 L ^(2))`