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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 = s2am

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 = s2am yields

at = [s2am][2am] = 2asm                  ..............(iii)

So that a = a2R + a2t = [2as2mR]2 + [2asm]2

Hence a = 2asm1 + [sR]2

 F = ma = 2as1 + [sR]2

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