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A smooth spehre of radius R is made to t...

A smooth spehre of radius R is made to translate oin a straight line with a constant acceleration a. A particle kept on the top of the sphere is released rom there at zero velocity with respect to the sphere. Find the speed of the particle with respect to the sphere as a functon of the angle `theta` it slides.

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The correct Answer is:
A, B, C
FBD of particle `w.r.t.` sphere
.
`K_(f) = (1)/(2)mv_(r)^(2) =W_("All")`.
or `1/2mv_(r)^(2) =W_(N) + W_(F) + W_(mg)`
`= 0 + Fx + mgh`
`=(ma) (R sin theta) + mg [R(1-cos theta)]`
`v_(r) =sqrt(2gR(1 + sin theta -cos theta)))`.
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