Q.

A hollow non conducting sphere  A and a solid non conducting sphere  B of equal radius  'R' and masses m  and 2m are kept a large distance apart on a rough horizontal surface. Charge on the two spheres  A and  B are  Q and  2Q respectively. Charges are distributed uniformly and remain constant and uniform as the spheres come closer. Friction is sufficient to support pure rolling and the kinetic energy of the two spheres just before collision is  KA and  KB. Find  100×KAKB.

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answer is 168.

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Detailed Solution

Let  v1 and  v2 be the speeds of sphere A and B just before collision, then from conservation of energy,

0=12mv12(1+23)+12(2m)v22(1+25)+K.Q(2Q)2R 0=56mv12+72mv22K.Q2R 56mv12+72mv22=K.Q2R  ...............(i)

From conservation of angular momentum about any point ‘O’

0=mv1R+23mR2(v1R)2mv2R25(2m)r2(v2R) v1=4225v2     ..............(ii)

Solving equation (i) and (ii) 

KB=25KQ267R KA=42KQ267R

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