A section of fixed smooth circular track of radius `R` in vertical plane is shown in the figure. A block id 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. `(R)/(2)`

Answer

C

Explanation

`h_(AB)=Rcos37^(@)-Rcos53^(@)`

`=8.0R-0.6R`
`=0.2r`
`v_(B)=sqrt(2gh_(AB))=sqrt(0.4gR)`
`a_(_|_)=gcos37^(@)=(0,.8g)=(v_(B)^(2))/(r)=(0.4gR)/(r)`
:. `r=`radius of curvature at `B`
`=(R)/(2)`