A small block of mass m, can move without friction on the outside of a fixed vertical circular track of radiusR. The block is attached to a spring of natural length `R//2` and spring constant K. The other end of spring is connected to a point at height `R//2` directly above the centre of track.
If the block is released from rest when the spring is in horizontal state (see figure) then at that moment,

Options

A. tangential acceleration is g `sqrt(3)/2-(kR)/(4m)(sqrt(3)-1)`
B. radial acceleration is `g/2+(kRsqrt(3))/(4m)(sqrt(3)-1)`
C. tangential acceleration is `g/2-(kRsqrt(3))/(4m)(sqrt(3)-1)`
D. radial acceleration is `gsqrt(3)/2-(kR)/(4m)(sqrt(3)-1)`

Answer

A

Explanation

`F_(t)=mgsintheta-kxcostheta,theta=60^(@)`
`a_(t)=gsin60^(@)-(kx)/mcos60^(@)=sqrt((3)g)/2-(kR)/(4m)(sqrt(3)-1)`
`a_(c)=v^(2)//r=0` released from rest