A partical is projected along a horizontal field whose co-efficient of friction varies $\mu = \large\frac{A}{x^2}$ where x is a distance from origin in meters and A is a positive constant. The initial distance of particle is 1m from orgin and its velocity is radially outwards. The minumum initial velocity at this point so that the particle never stops is

Question

$$(a)\;\sqrt {2gA} \quad (b)\;\infty \quad (c)\; 2 \sqrt {gA} \quad (d)\;4 \sqrt {gA}$$