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:

Options

A. `(5Kq^(2))/(4r)`
B. `(5Kq^(2))/(2r)`
C. `(5Kq^(2))/(3r)`
D. none of these

Answer

C

Explanation

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)`