1is the answer v=x0√2g/L
A rope with length L and mass density σ kg/m hangs over a massless
pulley. Initially, the ends of the rope are a distance x0 above and below
their average position. The rope is given an initial speed. If you want
the rope to not eventually fall off the pulley, what should this initial
speed be?
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UP 0 DOWN 0 0 3
3 Answers
1let the length of rope on one side be i and on other side be l-x0
mass of string on one side =lσ
mass of string on other side =(l-x0
for string to remain on pulley,the length must be equal on both side i.e one side go up by x0/2
and oter side come down by x0/2.
accln. of string as it moves from l-x0 to l-x0+dl
lσg-T=lσa
T-(l-x0)σg=(l-x0)σa
solving a=x0σg/(2lσ-x0σ)
final vel=0
u2=2as
=2∫x0σg/(2lσ-x0σ)
integrating betn limits 0 and x0/2 ,u can be calculated