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

A, B, C

Explanation

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))`