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. `2a[1+(s^(2)/(R^(2))]^(1//2)s`
C. `2as`
D. `2a[(R^(2))/(s)]^(1//2)`

Answer

B

Explanation

`K=as^(2)`
`(1)/(2)mv^(2)=as^(2)impliesv=sqrt((2a)/(m))simplies(dv)/(ds)=sqrt((2a)/(m))`
`a_(t)=v(dv)/(ds)=sqrt((2a)/(m))ssqrt((2a)/(m))=(2as)/(m)`
`a_(c)=(v^(2))/(R )=(2as^(2))/(mR)`
Total acceleration `a_(0)=sqrt(a_(t)^(2)+a_(c)^(2))=(2as)/(m)sqrt(1+((s)/(R ))^(2))`