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A uniform electric field $\bar{E} = - 400 \sqrt{3} \hat{y} N / C$ is applied in a region. A charged particle of mass m carrying positive charge q is projected in this region with an initial speed of $2 \sqrt{10} \times 10^{6} m / s .$ This particle is aimed to hit a target T which is 5m away from its entry point into the field as shown. Take $\frac{q}{m} = 10^{10} C / k g,$ then the

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Particle will hit $' T'$ if $θ = 45 °$

Particle will hit T if either $θ = 30 ° or 60 °$

Time taken by the particle to hit T could be $\sqrt{\frac{5}{6}} μ s$ as well as $\sqrt{\frac{5}{2}} μ s$

Time taken by the particle to hit T is $\sqrt{\frac{5}{3}} μ s$

answer is B, C.

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Detailed Solution

$a_{y} = \frac{q E_{y}}{m} = - 400 \sqrt{3} \times 10^{10}$

Range, $R = \frac{u^{2} \sin 2 θ}{a_{y}}$
Solving for $θ, θ = 30 ° or 60 °$
Time of flight, if $θ = 30 °, T_{1} = \frac{24 \sin θ}{a_{y}} = \sqrt{\frac{5}{6} μ s}$
If $θ = 60 °, T_{2} = \sqrt{\frac{5}{2} μ s}$

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