Kinetic energy of a particle moving along a circle of radisu R depends on the distance covered as `K =as^(2)` where a is a constant . Find the force acting on the particle as a function of s.

Options

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

Answer

B

Explanation

`k = as^(2) rArr 1/2 mv^(2) = as^(2)`
`rArr v = ssqrt((2a)/m)`
Radial acceleration, `a_(R) = v^(2)/R = (2as^(2))/(mR)`
Tangential acceleration, `a_(t) = (dv)/(dt) = (dv)/(ds). (ds)/(dt) = v(dv)/(ds)`
`rArr a_(t) = ssqrt((2a)/m).d/(ds)[ssqrt((2a)/m)] = ssqrt((2a)/m) sqrt((2a)/m) = (2as)/m`
Net acceleration,
`a =(2as)/m [1 + s^(2)/R^(2)]^(1/2)`
Force `F = ma = 2as (1 + s^(2)/R^(2))^(1//2)`