A chain of length L and mass per unit length `rho` is piled on a horizontal surface. One end of the chain is lifted vertically with constant velocity by a force P.

Options

A. P as function of height x of the end above the surface will be `rho(gx+v^(2))`
B. no energy will loss in this process.
C. work done by force will be `1/2rhogL^(2)+rhov^(2)L`
D. loss in energy `1/2rhogLv^(2)`

Answer

A, C, D

Explanation

`F_(ext)=V_(rel)(dm)/(dt)+m(dv)/(dt)`
`(dv)/(dt)=0`(v is contant)
`P=rhoxg+rhov^(2)`
`w_(P)+w_(g)=DeltaKE`
`w_(P)=+underset0oversetLint rhoxgdx+underset0oversetLint(rhodx)v^(2)`
`w_(P)=(rhoL^(2)g)/2+rhoLv^(2)`