The kinetic energy k of a particle moving along a circle of radius R depends on the distance covered. It is given as KE =a s^2 , where a is a constant. The force acting on the particle is

Step-by-step solution

In non-uniform circular motion two forces will work on a particle F_c and F_t . So, the net force F_ Net = F_c^2+F_t^2 ...(i) Centripetal force F_c= m v^2 R = 2 a s^2 R ...(ii) [given 1 2 m v^2=a s^2 given] Again from 1 2 m v^2=a s^2 v^2= 2 a s^2 m v=s 2 a m Tangential acceleration a_t= d v d t = d v d s d s d t a_t= d d s [s 2 a m ] va_t=v 2 a m =s 2 a m 2 a m = 2 a s m and F_t=m a_t=2 a s ...(iii) Now, on substituting value of F_c and F_t in Eq. (i), we get F_ Net = ( 2 a s^2 R )^2+(2 a s)^2 =2 a s [1+ s^2 R^2 ]^