A smooth circular tube of radius is fixed in a vertical plane

PHYSICS · Subjective · CBSE · Physics · Laws of Motion · Laws of Motion

Problem

A smooth circular tube of radius rr is fixed in a vertical plane. A particle is projected from its lowest point with a velocity just sufficient to carry it to the highest point. Show that the time taken by the particle to reach the end of the horizontal diameter is rgln⁡(1+2)\sqrt{\frac{r}{g}}\ln(1+\sqrt{2}).

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