A wire of cross sectional area 4xx10^(-4) m^2 modulus of rigidity 2xx10^(11) N//m^2 and length 1 m is stretched between two vertical rigid poles. A mass of 1kg is suspended at its middle. Calculate the angle it makes with horizontal. Given g = 10 ms^(-2)

A wire of cross sectional area 4xx10^(-4) m^2 modulus of rigidity 2xx1

1.	A wire of cross sectional area 4xx10^(-4) m^2 modulus of rigidity 2xx10^(11) N//m^2 and length 1 m is stretched between two vertical rigid poles. A mass of 1kg is suspended at its middle. Calculate the angle it makes with horizontal. Given g = 10 ms^(-2)
Answer» Solution :Refer to for equilibrium position of mass M, `Mg = 2T sin theta…… (i)` if `theta` is small, sin `theta ~~ theta = x//L….. (ii)` `As, T = (YA)/(L) DELTA L = (YA)/(L)[(L^2 + x^2)^(1//2)-L]` From (i) `Mg = (2YA x^2)/(2L^2) xx sin theta = YA theta^2 xx theta= YA theta^3` or `theta = ((Mg)/(YA))^(1//3) = [(1xx10)/(2xx 10^(11)xx4 xx10^(-4))]^(1//3)` `~~ 0.005 rad`