Question

A table with a smooth horizontal surface is fixed in a cabin that rotates with a uniform angular velocity ω in a circular path of radius R. A smooth groove AB of length L (<

Answer 1

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Question ⇒ A table with a smooth horizontal surface is fixed in a cabin that rotates with a uniform angular velocity ω in a circular path of radius R. A smooth groove AB of length L (<<R) is made on the surface of the table. The groove makes an angle θ 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.

Solutions ⇒  Centripetal acceleration acting on the Table = ω²r

∴ Its Component on AB = ω²r Cosθ

Now,  Using second equation of the Motion,  

S = ut + 1/2 at²

⇒ L = 0 + 1/2 ×  ω²r Cosθ t²

⇒ t² = 2L/ω²r Cosθ

∴ t = √(2L/ω²r Cosθ)

Hope it helps.

Answer 2

Answer:

Explanation:

The solution is given in the attachment