Question #5073f

1 Answer
Dec 6, 2017

#W.D_("when" 'n=4)rArr(MgL)/(32)#

Explanation:

Lets take a general situation:

Let a chain of mass M and length L is held on a frictionless table in such a way that #1/n#th part is hanging below the edge.

The portion hanging from the table is #L/n#

Required work done#=#change in potential energy of chain

Now,let Potential energy (U)#=#0 at the table level.

Potential energy initial#rArr#mgh { h is the length of the
hanging portion from centre of mass]

For regularly shaped uniform bodies, P.E change can be calculated by considering their mass to be centered at the geometrical point.

#h=L/(2n)#

Mass of #L# length is M

Mass of #L/n# length is #M/LxxL/n=M/n#

#U_i=-mgh=-mg{L/(2n)}=-{M/n}g{L/(2n)}=-(MgL)/(2n^2)#

#U_f=0#

Therefore required work done#=U_f-U_i=color(red){(MgL)/(2n^2)}#

#W.D_("when" 'n=4)rArr(MgL)/(32)#