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A hemispherical sheli of mass M and radius R made to vibrate as shown in figure. Find its frequency of oscillation. |
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Answer» Solution :CENTRE of mass of the hemispherical shell is at a distance `R//2` from the centre of hemisphere. `:.` The TORQUE in displaced position in `Mg"(R )/(2) sintheta` `M.I.` of the hemispherical shell about the AXIS passing through `O` is `(2MR^(2))/(3)`. (same as the `M.I.` about a diameter of the base as they are equidistant from the centre of mass) `rArr IALPHA= -Mg.(R )/(2)sintheta` (Torque and `theta` oppositely directed) `rArr (2)/(3)MR^(2)alpha=-Mg"(R )/(2)theta`(`theta` is small ) `alpha=(3)/(4)(g)/(R )theta` `OMEGA^(2)=(3)/(4)(g)/(R )` `T=2pisqrt((4R)/(3g))=4pisqrt((R )/(3g))` 
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