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Three particles having charges `q,q` and `2q` have masses m, 2m and 5 m respectively as shown, the three collinear charges are initially released from rest from the positions as shown. (Take `K=(1)/(4pi in_(0))` Q. The maximum kinetic energy of charge of mass 5m is:A. `(5Kq^(2))/(4r)`B. `(5Kq^(2))/(2r)`C. `(5Kq^(2))/(3r)`D. none of these |
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Answer» Correct Answer - C The ratio of velocities of acceleration of mass `m`, 2m and 5m are `-3:-1:1` considering left direction to be negative and right direction to be positive. Hence the distance between `m` and 2 m at any instant is sae as distance between 2m and 5 m. As thhe separation between charges becomes very large the loss in potential energy is equal to `(kq^(2))/(r)+(k2q^(2))/(r)+(k2q^(2))/(2r)=(4kq^(2))/(r)` and this equals to gain in kinetic for all the three charged particles. that is `(1)/(2)mxx(3x)^(2)+(1)/(2)2mxxv^(2)+(1)/(2)5mxxv^(2)=(1)/(2)16mxx` `v^(2)=(4kq^(2))/(r)` `because(1)/(2)5mv^(2)=(5Kq^(2))/(4r)` |
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