What will be the force acting on a particle moving along a circle of radius R , if its kinetic energy k depends on the distance covered as k = a s 2 ?

Question

What will be the force acting on a particle moving along a circle of radius R , if its kinetic energy k depends on the distance covered as k = a s 2 ?, 2 a R 2 s, 2 a s 1 + s 2 R 2 1 2, 2 a s 2 R, 2 a s

MARKS App · Accepted Answer

Given, 1 2 m v 2 = a s 2 ⇒ v = s 2 a m ∴ a R = v 2 R = 2 a s 2 m R .... (i) a t = d v d t = d v d s . d s d t = v d v d s .... (ii) From equation (i) a t = s 2 a m 2 a m = 2 a s m ..... (iii) So, net accelerations = a R 2 + a t 2 = 2 a s 2 m R 2 + 2 a s m 2 Hence, a 0 = 2 a s m 1 + s R 2 ∴ F = m a 0 = 2 a s 1 + s R 2

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