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A vertical rod 2m long, firxed at the u...

A vertical rod `2m` long, firxed at the upper end, is `13cm^(2)` in area for `'1m'` and `20 cm^(2)` in areqa for `1 m`. A colklar is attached to the free end. Through what height can a load of `100 kg` fall on to collar to cause maximum stress of `50N//mm^(2). Y = 200000 n//m^(2). (g = 9.8 m//s^(2))`

Text Solution

Verified by Experts

The correct Answer is:
`1.33 cm`
`(1)/(k) = (1)/(k_(1)) + (1)/(k_(2)), k_(1) = (A_(1)Y)/(l), k_(2) = (A_(2)Y)/(l), l = 1 m`
`k = (k_(1)k_(2))/(k_(1) + k_(2)) = (A_(1)A_(2))/((A_(1) + A_(2))) (Y)/(l)`
`k = (52)/(33) xx 10^(8)`
`F = 50 xx 10^(6) xx 13 xx 10^(-4) = 650 xx 10^(2)N`
`F = kx`
`x = (165)/(4) xx 10^(-5)m, mg (h + x) = (1)/(2) kx^(2) = (F^(2))/(2k)`
on solving `h = 1.33 cm`
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