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

A particle is projected along a horizontal field whose coefficient of

1.	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 isA. `infty`B. `2 sqrt(gA)`C. `sqrt(2 gA)`D. `4 sqrt(gA)`
Answer» Correct Answer - C 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)`.

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