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Question

A long smooth cylindrical pipe of radius r is tilted at an angle alpha to the horizontal. A small body at point A is pushed upwards along the inner surface of the pipe so that the direction of its initial velocity forms an angle phi with generatrix AB. Determine the minimum initial velocity V at which the body starts moving upwards without being separated from the surface of the pipe

Joshi sir comment

At the front of the cylinder, see a tilted circle $N o w c o m p a r e t h i s p r o b l e m w i t h v e r t i c a l c i r c u l a r m o t i o n . A i s t h e t o p p o i n t o f t h a t p a t h . W e k n o w t h a t t h e m i n i m u m v e l o c i t y a t t o p p o i n t \tan g e n t i a l t o p a t h o f v e r t i c a l c i r c l e s h o u l d b e \sqrt{g r} . H e r e d u e t o t i l t o f t h i s c i r c l e e f f e c t i v e g r a v i t y = g \cos α s o v \sin φ = \sqrt{g \cos α r} n o w s o l v e i n f o r m f o r a n y i s s u e w a i t f o r v i d e o$

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