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## Homework Statement

At a lunar base,a uniform chain hangs over the edge of a horizontal platform.A machine does ##1.0J## of work in pulling the rest of the chain onto the platform.The chain has a mass of ##2.0 kg## and a length of ##3.0m##.What length was initally hanging over the edge ? On the moon,the gravitational acceleraiton is ##\frac 1 6## of ##9,8 \frac {m} {s^2}##

## Homework Equations

##ρ_{chain}=M/L##

##W_g=-ΔU_g##

## The Attempt at a Solution

Let's suppose ##L_1## length is needed to pull.

So chain density will be ##ρ=\frac {2kg} {3m}=0.66\frac {kg} {m}##

The mass of ##L_1## is## L_1ρ=M_1##

The gravitational work on ##M_1## is ##W_g## which its ##-M_1gL_1=1J##

##(L_!)^2ρg=6J##

which ##L_1=1.05m## but the answer is ##1.4m##

Theres a "-" sign which makes me uncomfortable.Also I am making wrong at some point