The kinetic energy K of a particle moving along a circle of radius R depends on the distance covered s, as K = a s 2 , where, a is constant. Then the force acting on the particle is

Step-by-step solution

According to given problem, 1 2 m v 2 = a s 2 ⇒ v = s 2 a m So, a c = v 2 R = 2 a s 2 m R ... (i) Further more as a t = d v d t = d v d s . d s d t = v × d v d s ... (ii) [by chain rule] Which in light of Equation. (i) i.e. v = s 2 a m yields a t = s 2 a m 2 a m = 2 a s m ... (iii) So that a = a R 2 + a t 2 = 2 a s 2 m R 2 + 2 a s m 2 Hence, a = 2 a s m 1 + s R 2 ∴ Force acting on the particle F = m a = 2 a s 1 + s R 2