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If a compressive force of 3.0xx10^(4)N i...

If a compressive force of `3.0xx10^(4)N` is exerted on the end of a 20 cm long bone of cross-sectional area `3.6cm^(2)` (i) will the bone break and (ii) if not by how much length does it shorten? Given compresive strength of bone `=7.7xx10^(8)N//m^(2)` and young's modulus of bone `=1.5xx10^(10)N//m^(2)`

Text Solution

Verified by Experts

The correct Answer is:
No,` (10)/(9) xx 10^(-3)m = 1.11 mm`.
(a) `sigma = (F)/(A) = (3 xx 10^(4))/(3.6 xx 10^(-4)) = (30)/(36) xx 10^(8) = (5)/(6) xx 10^(8) lt 7.7 xx 10^(8) n//m^(2)`
hence it will not break.
(b) `Deltal = (FL)/(AY) = (3 xx 10^(4) xx 20 xx 10^(-2))/(3.6 xx 10^(-4) xx 1.5 xx 10^(10)) = (40 xx 10^(-4))/(3.6) = (10)/(9) xx 10^(-3)m`
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