(d) Given, mass of both particle =m Charge of particle, A=+q Charge of particle, B=+4q Potential difference =V Kinetic energy is given by K=‌
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mv2‌‌‌⋅⋅⋅⋅⋅⋅⋅(i) This energy is equal to electrostatic potential energy is K=V×Q‌‌‌⋅⋅⋅⋅⋅⋅⋅(ii) From Eqs. (i) and (ii), we have ‌
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mv2=V×Q For particle A, qV=‌
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mvA2‌‌‌⋅⋅⋅⋅⋅⋅⋅(iii) For particle B, 4qV=‌
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mvB2‌‌‌⋅⋅⋅⋅⋅⋅⋅(iv) Dividing Eq. (iii) by Eq. (iv), we get ‌