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A uniform chain of total length 2L hangs in equilibrium over a small, smooth pulley (the string is inextensible). End B is given a slight downward displacement, causing the chain to accelerate. Find the acceleration of end B when it has been displaced a distance x from the equilibrium position.

1. x/L g
2. 2x/L g
3. x/(2L) g
4. g

Correct answer: x/L g

Solution

Let linear mass density be lambda. Unbalanced weight = lambda*(2x)*g (the extra length 2x on the heavier side). Total mass = lambda*2L. So a = (lambda*2x*g)/(lambda*2L) = (x/L) g.

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