A table with smooth horizontal surface is fixed in a cabin that rotates with a uniform angular velocity 
in a circular path of radius R (figure). A smooth groove AB of length L (< < R) is made on the surface of the table. The groove makes an angle 
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 the particle to reach the point B.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Sol. Centripetal acceleration at A = ω 2 R
acceleration along AB = ω 2 R cos θ
Time taken to reach the point B
L = 0 + 
( ω 2 R cos θ ) t 2 (L << R)
t = 
Ans.
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