A particle of mass M is moving in a circular path of radius 2m. Its speed depends on the distance covered by the particle from the hegining according to the relation c = ks, where k is a positive constant and s is the distance covered. The power of force acting on teh particle when the particle has covered half of the circular path will be :

Options

A. `pi^(2)k^(2)M`
B. `2pi^(2)k^(3)M`
C. `4pi^(2)k^(3)M`
D. `8pi^(2)k^(2)M`

Answer

C

Explanation

P = Fv
`S = pi R`
`v = ks rArr v = k.pi R`
`a = v (dv)/(ds) = ks.k = k^(2)s`
`s = piR`
`a = k^(2).piR rArr F = mk^(2). pi R`
`P = mk^(2) pi R . kpi R = mk^(3) pi^(2)R^(2)`
`M = 4 pi^(2)k^(3)m`