A small ball is rolled with speed u from point A along a smooth circular track as shown in figure. If x=3R, then determine the point of projection after passing through C, the highest point.
A
32√gR
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B
12√gR
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C
53√gR
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D
52√gR
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Solution
The correct option is D52√gR
From C the ball becomes a horizontal projectile with range x=3R and height H=2R. Thus, x=v√2(H)g 3R=v√2(2R)g ⇒v=32√gR
Conserving mechanical energy from B to C. KB+UB=KC+UC 12mu2+0=12mv2+mg(2R) u2=94gR+4gR⇒u=52√gR