Question

Two particles of masses m and 2 m with charges 2q and 2q are placed in a uniform electric field E and allowed to move for the same time. The ratio of their kinetic ener8ies will be

Moderate

Solution

$a_{1} = \frac{2 qE}{m} and a_{2} = \frac{2 qE}{2 m} ∴ a_{1} = 2 a_{2} K_{1} = \frac{1}{2} m_{1} v_{1}^{2} = \frac{1}{2} m_{1} {(a_{1} t)}^{2} (∵ v = u + at) \begin{aligned} K_{2} = \frac{1}{2} m_{2} {v_{2}}^{2} = \frac{1}{2} m_{2} {(a_{2} t)}^{2} \\ ∴ \frac{K_{1}}{K_{2}} = \frac{m_{1} {a_{1}}^{2}}{m_{2} {a_{2}}^{2}} = \frac{m}{2 m} \times \frac{4}{1} = \frac{2}{1} . \end{aligned}$

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