Question

A chain of length L is suspended from a strip of rubber of natural length hand is in equilibrium in the position shown in fig. The chain is then cut at point A. Determine the length x knowing that the top of remaining portion of the chain will rise sufficiently to just touch the ceiling

Answer 1

firstly it is given that a chain of length (L) suspended from strip

mg= k (2h-h)=kh---(1)

after cutting the chain at point A

1/2$kh^{2}$=mxg x 2h

hence kh=4mxg----(2)  

by equating or solving 1 and 2 we get

mx=m/4

x=L/4

Answer 2

Given:

The chain of length L is suspended from a strip of rubber.

To Find:

the length x of the remaining portion

Solution:

⇒ mg = k(2h-h) = kh ..(i)

⇒ 1/2kh² = mxg × 2h    [it is given that the chain was cut in half]

⇒ kh = 4m × 2h ..(h)

using equation (i) and (ii)

⇒ mx = m/4

⇒ x = L/4

Therefore, the length x of the chain = L/4