Question

Question #5073f

Answer 1

`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)`