JEE Main · 2021 · 26 Aug 2021 · Shift 1 · Work, Power & Energy

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A uniform chain of length 3 meter and mass 3 kg overhangs a smooth table with 2 meter laying on the table. If k is the kinetic energy of the chain in joule as it completely slips off the table, then the value of

k

is ______ (Take

g = 10 m / s^{2}

)

Answer: 40

Solution

The chain has linear density

λ = \frac{3}{3} = 1

kg/m, and heights are measured from the table top. Initially

1

m hangs with its centre of mass

0.5

m below the edge, so

U_{i} = - (1) (10) (0.5) = - 5 J

At the instant the chain leaves the table, the whole

3

kg hangs with its centre of mass

1.5

m below the edge, so

U_{f} = - (3) (10) (1.5) = - 45 J

The table is smooth, so the whole loss of potential energy appears as kinetic energy:

k = U_{i} - U_{f} = - 5 + 45 = 40 J

JEE Main · 2021 · 26 Aug 2021 · Shift 1 · Numerical answer

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