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 just after it leaves the track `B` is ?

Options

A. R
B. `( R)/(4)`
C. `( R)/(2)`
D. none of these

Answer

C

Explanation

Apply conservation of energy with `O` as reference level `mg (2r)/(5) +0 = (mgr)/(5)+(1)/(2)mv^(2)`
`v = sqrt((2gr)/(5))` , Radius of curvature `= (v_(1)^(2))/(a_(n))`
`(2gr//5)/(g cos37) = (r)/(2)`.