Chain and Elastic string problem

[Vibhor]

Homework Statement

A uniform chain of length L hangs from an elastic string of natural length L. The upper end of the string is connected with the ceiling .When the system is in equilibrium , the string stretches by an amount L .At what distance from the lower end of the chain ,the chain should be cut so that upper end of chain just strikes the ceiling?

Homework Equations

The Attempt at a Solution

'k' is the force constant of the string and m is the mass of the chain.

From equilibrium condition kL = mg → k=mg/L

Suppose the chain is cut a distance 'x' from below .

Applying COE , (1/2)kL² = (m/L)(L-x)g(2L)

This gives x= (3/4)L .

Is it right ?

Many Thanks

 

[Simon Bridge]

You have argued that the energy stored in the string needs to be enough to throw the remaining mass through a height 2L ... that is well reasoned, well done.