Figure shows tracks of three charged particles crossing a uniform electrostatic field with same velocities along horizontal. Give the sign of the three charges. Which particle has the highest charge to mass ratio?

Explanation

Particles 1 and 2 are deflected towards the positive plate, which means that the charges carried by them must be negative. Particle 3 is deflected towards the negative plate, which means that its charge must be positive. Let us assume that y be the deflection along Y-axis when a particle travels distance x along X-axis. Let the initial velocity of the particle be u, which is perpendicular to electric field intensity E that is directed downwards in the given figure. Let us assume that the charge on the particle is q and its mass is m.
`S=1/2 at^2 rArr y=1/2 ((qE)/m) (x/u)^2`
According to the above result, the deviation along Y-axis is proportional to q/m. In the given figure, we have the largest deviation for particle 3, hence the highest charge to mass ratio must be associated with particle 3.