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A triangular of rigid wire frame 'AOB' is made, in which length of each wire is l and mass m. The whole system is suspended from point O and free to perform SHM about x-axis or about z-axis. When it performs SHM aboutx-axis its time period of oscillation is T_(1) and when it performs SHM about z-axis, its time-period of osciallation is T_(2), then choose the correct option. |
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Answer» `T_(1) lt T_(2)` CASE I : System is performing SHM about `x-`AXIS `I_(X)=I_(AB)+I_(AO)+I_(BO)=(3ML^(2))/(4)+[(ml^(2))/(3)sin^(2)60^(@)]xx2=(5ml^(2))/(4)` `T_(1)=2pisqrt((I_(x))/(M_(sys)gd))=2pisqrt(((5ml^(2))/(4)xxsqrt(3))/(3mxxgxxl))=2pisqrt((5sqrt(3)l)/(12g))` Case II : System is performing SHM about `z-` axis `I_(z)=I_(AB)+I_(AO)+I_(BO)=[(ml^(2))/(12)+m((sqrt(3)l)/(2))^(2)]+(ml^(2))/(3)+(ml^(2))/(3)=ml^(2)[(1)/(12)+(3)/(4)+(2)/(3)]` `=ml^(2)[(1+9+8)/(12)]=(3ml^(2))/(2)` `T_(2)=2pisqrt((I_(z))/(M_(sys)gd))=2pisqrt((3ml^(2)xxsqrt(3))/(2xx3mxxgxxl))=2pisqrt((sqrt(3)l)/(2g))` |
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