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

Answer

B

Explanation

`(1)/(2)mv^(2)=as^(2)`
`v^(2)=(2as)/(m)`
`v=sqrt((2a)/(m))s`
`a_(r)=v(dv)/(ds)=sqrt((2a)/(m))ssqrt((2a)/(m))-((2a)/(m))s`
`F_(T)=ma_(T)=2as`
`F_(C)=(mv^(2))/(R)=(2a)/(R)s^(2)`
`F=sqrt(F_(T)^(2)+F_(C )^(2))=sqrt((2as)^(2)+((2as^(2))/(R))^(2))`
`F=2assqrt((1+(s^(2))/(R^(2))))`