Questions

# A uniform rod is rotating about one of its end with a constant angular velocity $\mathrm{\omega }$ in gravity free space. The radial strain produced in two halves is $\mathrm{k}\left(>1\right)$. Then find the value of $\frac{20\mathrm{k}}{11}$.

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a
1
b
2
c
3
d
4

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detailed solution

Correct option is D

dL=TAYdx=mω22ALYdx  ∵T=mω22LL2-x2 ∴∆L=mω22ALYL2x-x33 ∆L for entire rod=k.2L33=k = constant ∆L for first half =kL312-124=11kL324 ∆L for second half=kL323-1124=524kL3 ∴k=115 ∴20k11=4

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