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A light rod of length of length 2 m is ...

A light rod of length of length `2 m` is suspended from a 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 `10^(-3) m^(2)` and the other is of brass of cross- section `2xx10^(-3) m^(2).x` is the distance from the steel wire end, at which a weight may be hung. ` Y_(steel) = 2xx10^(11) Pa and Y_(brass) = 10^(11) Pa`
Which of the following statement(s) is /are correct ?

Text Solution

Verified by Experts

Given, stress in steel = stress in brass
`(T_(S))/(A_(S))=(T_(B))/(A_(B))`
`(T_(S))/(T_(B))=(A_(S))/(A_(B))=(10^(-3))/(2xx10^(-3))=(1)/(2)" …(i)"`
At the system is in equilibrium, taking moments about D, we have
`A_(S).x=T_(B)(4-x)`
`(T_(S))/(T_(B))=(4-x)/(x)" ...(ii)"`
From equations (i) & (ii)
`(4-x)/(x)=(1)/(2)`
`x=8-2x`
3x = 8
`x=(8)/(3)=2.67m`
Position is 2.67 m from the end, where steel wire is attached.
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