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# A rope of length 30 cm is on a horizontal rough table with maximum length hanging from edge ‘A’ of the table. The coefficient of friction between rope and table is 0.5. The distance of centre  of mass of the rope from ‘A’ is

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a
5153 cm
b
5173 cm
c
7153 cm
d
5193 cm

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detailed solution

Correct option is B

μl−lnmg=mglnμ1−1n=1n0.5n−1n=1nn−1=2;          n=3The total mass is m .The length of the rope hanging is  I3 and the length of the rope on the table is 2I3  whose mass is equal to2m3→rcm2m3−10i^+m3−5j^m=−20i^−5j^3rcm=4009+259=4259=5173

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