The kinetic energy of a particle moving along a circle of radius R depends on the distance covered s as T = KS2 where K is a constant. Find the force acting on the particle as a function of S -

Options

A. `(2as^(2))/(R)`
B. `2as(1+(s^(2))/(R^(2)))^(1//2)`
C. `as(1+(s^(2))/(R^(2)))^(1//2)`
D. None of these

Answer

B

Explanation

Given, `(1)/(2)mv^(2)=as^(2)`
or `F_(n)=(mv^(2))/(R)=(2as^(2))/(R)` ....(i)
Further,
`vsqrt((2a)/(m)).s`
or `a_(t)=(dv)/(dt)=sqrt((a)/(m)).(ds)/(dt)=sqrt((sa)/(m)).v`
`=sqrt((2a)/(m)).sqrt((2a)/(m)).s=(2as)/(m)`
`therefore" "F_(t)=ma_(t)=2as` ....(ii)
`therefore" "f_("net")=sqrt(F_(n)^(2)+F_(t)^(2))`
`=2as sqrt(1+(s^(2))/(R^(2)))`