A hollow non conducting sphere A and a solid non conducting sphere B of equal radius ' R ' and masses m and 2 m are kept at a large distance apart on a rough horizontal surface. Charge on the two spheres A and B are Q and -2 Q 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 sphe

Step-by-step solution

Let v ₁ and v ₂ be the speeds of sphere A and B just before collision, then from conservation of energy, aligned & 0= 1 2 mv ₁^2 (1+ 2 3 )+ 1 2 (2 ~m ) v₂^2 (1+ 2 5 )+ K Q (-2 Q ) 2 R & 0= 5 6 mv ₁^2+ 7 5 mv ₂^2- K Q ^2 R ; 5 6 mv ₁^2+ 7 5 mv ₂^2= K Q ^2 R aligned From conservation of angular momentum about any point ' O ' 0= mv ₁ R + 2 3 mR ^2 ( v ₁ R )-2 mv ₂ R - 2 5 (2 ~m ) r ^2 ( v ^2 R ) ; v ₁= 42 25 v ₂ Solving equation (i) and (ii) K _ B = 25 KQ ^2 67 R ; K _ A = 42 KQ ^2 67 R