A thin uniform copper rod of length l and cross-section area A and mass m rotates uniformly with an angular velocity `omega` in a horizontal plane abo

Question

A thin uniform copper rod of length l and cross-section area A and mass m rotates uniformly with an angular velocity `omega` in a horizontal plane abo

A thin uniform copper rod of length l and cross-section area A and mass m rotates uniformly with an angular velocity `omega` in a horizontal plane about a vertical axis passing through one of its ends. The elongation of the rod will be
A. `(momega^(2)l^(2))/(6AY)`
B. `(momega^(2)l^(2))/(3AY)`
C. `(momega^(2)l^(2))/(AY)`
D. `(momega^(2)l^(2))/(2AY)`

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - C
Free expansion of rod = `alphaLDeltatheta=15 xx 10^(-6)xx2(50-20)=15xx10^(-6)xx2xx30=0.9mm`
If expansion is fully prevented Strain = `(DeltaL)/(L)=(9xx10^(-4))/(2)=4.5 xx10^(-4)`
Thermal stress = (strain)Y = `(4.5 xx 10^(-4))(2xx10^(11))=9xx10^(7)N//m^(2)`

5 views Answered 2023-02-05 15:29