A steel wire of area of cross-section A and length 2L is clamped firmly between two points seperated by a distance .2L.. A body is hung from the middle point of the wire such that the middle point sags by a distance x. Calculate the mass of the body and the angle made by string with the horizontal

A steel wire of area of cross-section A and length 2L is clamped firml

1.	A steel wire of area of cross-section A and length 2L is clamped firmly between two points seperated by a distance .2L.. A body is hung from the middle point of the wire such that the middle point sags by a distance x. Calculate the mass of the body and the angle made by string with the horizontal
Answer» SOLUTION : Since .`theta`. is small `sin theta = tan theta=(X)/(L)` `y=(F)/(A).(L)/(e )` `F=(YA e)/(L)=(YA)/(L)[(L^(2)+x^(2))^(1//2)-L]` `F=(YA)/(L)[L(1+(x^(2))/(2L^(2)))-L]=(YA)/(L)[L+(x^(2))/(2L)-L]` `F=(YA x^(2))/(2L^(2)) , 2T sin theta=Mg` `2(T)theta=Mg""(because " for small ANGLES "sin theta=theta)` `2Ftheta =Mg "" 2.(YA x^(2))/(2L^(2))theta=Mg` `(2YA x^(2))/(2L^(2)). (x)/(L)=Mg, ""M=(YAX^(3))/(L^(3)g)` `(x)/(L)=((Mg)/(YA))^(1//3), "Tan" theta=(x)/(L)` `"Tan"theta=((Mg)/(YA))^(1//3) rArrtheta ="Tan"^(-1)((Mg)/(YA))^(1//3)`