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Darpan Fakaruddin Dasgupta
Asked: 2022-11-11T05:47:34+05:30 In:

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Consider a uniform chain of mass `m` and length `L`, the chain is released when hanging length is `L_0`. Find the speed with which the chain leaves the table.

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Consider a uniform chain of mass `m` and length `L`, the chain is released when hanging length is `L_0`. Find the speed with which the chain leaves the table.
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  1. `K_1=0`,`U_1=-(1)/(2)((m)/(L)L_0)gL_0`
    `K_2=(1)/(2)mv^2`,`U_2=-(mgL)/(2)`
    By mechanical energy conservation
    `K_1+U_1=K_2+U_2`
    `0-(mgL_0^2)/(2L)=(1)/(2)mv^2-(mgL)/(2)`
    `v^2=gL-(gL_0^2)/(L)=(g(L^2-L_0^2))/(L)`
    `v=sqrt((g(L^2-L_0^2))/(L))`

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