A section of fixed smooth circular track of radius R in vertical plane is shown in the figure. A block is released from position A and leaves the track at B . The radius of curvature of its trajectory when it just leaves the track at B is-

Question

A section of fixed smooth circular track of radius R in vertical plane is shown in the figure. A block is released from position A and leaves the track at B . The radius of curvature of its trajectory when it just leaves the track at B is-, R, R / 4, R / 2, none

MARKS App · Accepted Answer

In figure O C = R cos ⁡ 53 ° = 3 R 5 ; O E = R cos ⁡ 37 ° = 4 R 5 So C E = R 5 From A to B , 1 2 m v 2 = m g R 5 [Energy conservation] v = 2 g R 5 Let radius of curvature at B is r g cos ⁡ 37 ° = v 2 r r = v 2 g cos ⁡ 37 ° = 2 g R 5 × 10 × 4 / 5 = R 2

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