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Question

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
32gR
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B
12gR
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C
53gR
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D
52gR
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Solution

The correct option is D 52gR

From C the ball becomes a horizontal projectile with range x=3R and height H=2R. Thus,
x=v2(H)g
3R=v2(2R)g
v=32gR
Conserving mechanical energy from B to C.
KB+UB=KC+UC
12mu2+0=12mv2+mg(2R)
u2=94gR+4gRu=52gR

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