The kinetic energy K of a particle moving along a circle of radius R depends upon the distance s as `K=as^2`. The force acting on the particle is

Options

A. `2as^(2)/R`
B. `2as(1+ s^(2)/R^(2))^(1/2)`
C. `2as`
D. `2a`

Answer

`(2)`

Explanation

`1/2 mv^(2) = as^(2)
v^(2) = (2as^(2))/m, a_(c) = v^(2) /R = (2as^(2))/(mR)`
`2v dv/dt = 2a /m(2s)ds /dt `
`a_(t) = (2as)/m`
` F = ma_("net") = m sqrt((a_(c)^(2) + a_(t)^(2))`
`F = = m sqrt(((2as^(2))/(mR))^(2) + ((2as)/m)^(2)`
`F = 2as(1 + (s^(2))/(R^(2)))^(1/2)`