A particle is projected along a horizontal field whose coefficient of friction varies as `mu=A//r^2`, where r is the distance from the origin in meters and A is a positive constant. The initial distance of the particle is `1m` from the origin and its velocity is radially outwards. The minimum initial velocity at this point so the particle never stops is

Options

A. `infty`
B. `2 sqrt(gA)`
C. `sqrt(2 gA)`
D. `4 sqrt(gA)`

Answer

C

Explanation

If the particle never stops than it may move till `x = infty`
`(1)/(2) mv^(2) = underset(1) overset(infty) int mumgd.dx rArr (V^(2))/(2) = Ag underset(1) overset(infty) int (1)/(x^(2)) dx`
so, `V = sqrt(2gA)`.