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

Step-by-step solution

aligned W= U & =U_f-U_i=U_ -U_p & =-U_P & =-m V_P & =-V_P ( as m=1) aligned Potential at point P will be obtained by integration as given below Let d M be the mass of small ring as shown aligned d M & = M (4 R)^2- (3 R)^2 (2 r) d r & = 2 M r d r 7 R^2 d V_P & =- G d M 16 R^2+r^2 & =- 2 G M 7 R^2 _ 3 R ^ 4 R r 16 R^2+r^2 d r & =- 2 G M 7 R (4 2 -5) W & =+ 2 G M 7 R (4 2 -5) aligned correct option is (a).