A thin uniform disc (see figure) of mass M has outer radius 4R and inner radius 3R. The work required to take a unit mass for point P on its axis to infinity is

Options

A. `(2GM)/(7R) (4sqrt(2)-5)`
B. `-(2GM)/(7R)(4sqrt(2)-5)`
C. `(GM)/(2R)`
D. `(2GM)/(5R)(sqrt(2)-1)`

Answer

A

Explanation

`dm=(M(2pir)dr)/(pi(16R^(2)-9R^(2))4R)`
`dV=(-G(dm))/(sqrt(r^(2)+16R^(2))), V=int_(3R)^(4R) dV`
`W=m[V_(oo)-V]`