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A particle is projected along a horizont...

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

A

`oo`

B

`2sqrt(gA)`

C

`sqrt(2gA)`

D

`4sqrt(g A)`

Text Solution

Verified by Experts

The correct Answer is:
C
Work done against friction must equal the initial kinetic energy
`:. (1)/(2)mv^(2) = underset(1)overset(infty)(int) mu mgdx` ,
`(v^(2))/(2)=Ag underset(1)overset(infty)(int)(1)/(x^(2))dx , (v^(2))/(2)=Ag[-(1)/(x)]_(1)^(infty)`
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