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)/(4R)`
D. `(2GM)/(5R)(sqrt(2)-1)`

Answer

A

Explanation

`W= +int dv=+int(Gdm)(r^(2))`
`=-int_(3R)^(4R) (Gxx(M)/(pi(16R^(2)-9R^(2)))xx2pixxdx)/(sqrt(x^(2)+16R^(2)))`
`=(2GM)/(7R^(2))[4sqrt(2)-5]`