A light rod of length `2 m` is suspended from the ceiling horizontally by means of two vertical wires of equal length tied to its ends. One of the wires is made of steel and is of cross section `0.1 cm^(2)`. The other wire is a brass of cross section `0.2 cm^(2)`. A weight is suspended from a certain point of the rod such that equal stress are produced in both the wires. Which of the following are correct?

Explanation

Given, m=2kg, `omega=2pif=2pixx4=8pi "rads"^(-1),r=0.5` m

From the figure,
`T=" cos"theta=mg` and `T" sin"theta=(mv^(2))/(r)=momega^(2)`
Tension in cord
`T=sqrt((T" sin"theta)^(2)+(T" cos"theta)^(2))`
`=sqrt((momega^(2)r)^(2)+(mg)^(2))`
`T=sqrt([2xx(8pi)^(2)xx0.5]^(2)+[2xx10]^(2))=631 N`
The extension of cord,
`DeltaL=(TL)/(AY)=(631xx2)/(0.5xx10^(-4)xx10^(8))`
`=360xx10^(-4)m=3.60cm`