Question

# The kinetic energy k of a particle moving along a circle of radius R depends  on the distance covered s as k = as2 where a is a constant. The force acting  on the particle is

Solution

## The correct option is B According to given problem 12mv2 = as2 ⇒ v = s√2am So aR = v2R = 2as2mR               ..............(i) Further more as at = dvdt = dvds.dsdt = vdvds         ......................(ii) (By chain rule) Which in light of equation (i) i.e. v = s√2am yields at = [s√2am][√2am] = 2asm                  ..............(iii) So that a = √a2R + a2t = √[2as2mR]2 + [2asm]2 Hence a = 2asm√1 + [sR]2 ∴ F = ma = 2as√1 + [sR]2

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