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A hemispherical bowl of radius R is set ...

A hemispherical bowl of radius R is set rotating about its axis of symmetry which is kept vertical. A small block kept in the bowl rotates with the bowl without slipping on its surface. If the surfaces of the bowl is smooth, and the angle made by the radius through the block with the vertical is `theta`, find the angular speed at which the bowl is rotating.

Text Solution

Verified by Experts

Here ` OA = R, angleAOC = theta`
Block moves in a horizontal circle with centre `C` and
radius ` r = AC = R sin theta`
`:.` In equilibrium `N cos theta = mg`
and `N sin theta = m omega^(2) (R sin theta)`
`N = m omega^(2) R`
From(i) `m omega^(2) R cos theta = mg`
` omega = sqrt((g)/(R cos theta))`
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