In the figure shown strings AB and BC have masses m and 2m respectively. Both are of same length l.Mass of each string is uniformly distributed on its length. The string is suspended vertically from the ceiling of a room.A small jerk wave pulse is given at the end 'C'.It goes up to upper end 'A' in time 't' .If the value of t is given by `a sqrt(l/g)+b sqrt(l/g)(sqrtc-sqrtd)` then a+b+c+d is

Explanation

For part BC
`v=sqrt(T/mu)=sqrt((m//l.y.g)/(m//l))=sqrt(y.g)`
`rArr (dt)/(dt)=sqrt(y.g)=int_0^l(dy)/sqrty=int_(0)^(t_(1))sqrtg dt`
`rArr 2sqrtl=sqrtg.t_1`
`rArr t_1`=time to go from C to B=`2sqrt(l/g)`
For part BA
`v=sqrt((2mg+m/l.y.g)/(m//l))=sqrt((2l+y)g)`
`(dy)/(dt)=sqrt((2l+y)g)rArr int_0^l (dy)/sqrt(2l+y)=int_0^(t_2)sqrtg dt`
`rArr2(sqrt3-sqrt2).sqrtl=sqrtg.t_2`
`rArr t_2`=time to go from B to A =`2(sqrt3-sqrt2).sqrt(l/g)`
`therefore` total time =`t_1+t_2=2sqrt(l/g)+2(sqrt3-sqrt2).sqrt(l/g)`