An elastic cord of constant K and length L is hung from point A having a massless lock at the other end. A smooth ring of mass M falls from point A , the maximum elongation of cord is

Options

A. `(mg)/(K)(1+(1+2KL)/(Mg))`
B. `(Mg)/(K)(1-(1-(2KL)/(Mg))^(1//2))`
C. `(MgL)/(K)`
D. `(Mg)/(K)(1+(1+(2KL)/(Mg))^(1//2))`

Explanation

[4]
Let extension in cord is X
`Mg(L+x)=(1)/(2)Kx^(2)`
`rArrKx^(2)-2Mgx-2MgL=0`
`x=(2Mg+-sqrt(4M^(2)g^(2)+8KMgL))/(2K)`
`=(Mg)/(K){1+sqrt((2KL)/(Mg))}`