A ball of mass 'm' is suspended from a point with a massless string of length `l` in form of a pendulum. This ball is given a horizontal velocity `sqrt(4 gl)` at bottom most point. When string makes an angle `60^(@)` from lower vertical, `(a_(c))/(a_(t))=p`. write the value of `p^(2)`. `(g=10 m//s^(2))`

Explanation

`a_(t)=g sin 60^(@)=(sqrt(3)g)/2`
`a_(c)=(v^(2))/R`
`1/2mv^(2)-mgRcos 60 =1/2 m(4gR)-mgR`
`1/2 mv^(2)=3/2 mgR`
`v^(2)=3gR`.
`a_(c)=(3gR)/R=3g,a_(t)=(sqrt(3)g)/2,a_(c)=3g`
`P=(a_(c))/(a_(t))=(2xx3g)/(sqrt(3)g)=2sqrt(3)`