A spring mass system (mass m, spring constant k and natural length l) rests in equilibrium on a horizontal disc. The free end of the spring is fixed at the centre of the disc. |
If the disc together with spring mass system, rotates about its axis with an angular velocity \[\omega ,\] \[(k>>m\,{{\omega }^{2}})\] the relative change in the length of the spring is best given by the option |
[JEE MAIN Held on 09-01-2020 Evening] |
A) \[\sqrt{\frac{2}{3}}\left( \frac{m{{\omega }^{2}}}{k} \right)\]
B) \[\frac{m{{\omega }^{2}}}{k}\]
C) \[\frac{m{{\omega }^{2}}}{3k}\]
D) \[\frac{2m{{\omega }^{2}}}{k}\]
Correct Answer: B
Solution :
[b] \[m{{\omega }^{2}}({{I}_{0}}+x)=kx\] |
\[x=\frac{m{{I}_{0}}{{\omega }^{2}}}{k-m{{\omega }^{2}}}\] |
For \[k>>m{{\omega }^{2}}\] |
\[\frac{x}{{{I}_{0}}}=\frac{m{{\omega }^{2}}}{K}\] |
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