The block of mass `m` initially at `x=0` is acted upon by a horizontal force at any position `x` is given as `F =a-bx^(2)(` where `a gt mu mg)`, as shown in the figure. The co`-` efficient of friction between the surface of contact is `mu`. The net work done on the block is zero, if the block travels a distance of `......................`

Answer

`x=[3(a-mu mg)//b]^(1//2)`

Explanation

`W_(f)+W_(F)=-mu mg x+underset(0)overset(x)int (a-bx^(2))dx`
`=(-mu mg +a)x-(bx^(3))/(3)`
`rArr x=sqrt((3(a-mu mg))/(b))`