A small ball is rolled with speed `u` from piont A along a smooth circular track as shown in figure. If `x=3R`, then

Determine the required speed u so that the ball returns to A, the point of projection after passing through C, the highest point.

Options

A. (a) `3/2sqrt(gR)`
B. (b) `1/2sqrt(gR)`
C. (c) `5/3sqrt(gR)`
D. (d) `5/2sqrt(gR)`

Answer

D

Explanation

Let the velocity at the point is `v_C`. Then for projectile motion from C to A,
`Rang e=v_csqrt((2(height))/(g))implies3R=v_csqrt((2xx2R)/(g))`
`impliesv_C=3/2sqrt(Rg)`
To find velocity at B, apply conservation of energy, i.e.,
`=1/2mv_B^2=mg2R+1/2mv_C^2=V_B=5/2sqrt(Rg)`