A table with smooth horizontal surface is fixed in a cabin that rotates with a uniform angular velocity `omega` in a circular pathof radius R. A smooth groove AB of length `L(ltltR)` is made on the surface of the table. The groove makes an angle` theta` with the radius OA of the circle in which the cabin rotates. A small particle is kept at the point A in the groove and is released to move along AB. Find the time taken by tehparticle to reach the point B.

A table with smooth horizontal surface is fixed in a cabin that rotate

1.	A table with smooth horizontal surface is fixed in a cabin that rotates with a uniform angular velocity `omega` in a circular pathof radius R. A smooth groove AB of length `L(ltltR)` is made on the surface of the table. The groove makes an angle` theta` with the radius OA of the circle in which the cabin rotates. A small particle is kept at the point A in the groove and is released to move along AB. Find the time taken by tehparticle to reach the point B.
Answer» Correct Answer - A::B::C The cabin rotates with angular velocity `omegas` and radius R. `:.` The particle experiences a force `mRomega^2`. The component of `mRomega^2` alogn the provided force to the particle to move along AB. `:. mRomega^2costheta=ma` `rarr a=Romega^2 cos theta` Length of groove L` L=ut+1/2at^2` `rarr L=1/2 Romega^2 cos theta t^2` `rarr t^2=(2L)/(Romega^2costheta)` `rarr t=sqrt((2L)/(Romega^2-costheta))`

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