A charged particle of mass $m = 1 k g$ and charge $q = 2 μ C$ is thrown from a horizontal ground at an angle $θ = 45^{0}$ with speed $20 m / s$ . In space a horizontal electric field $E = 2 \times 10^{7}$ V/m exists along the horizontal component of the velocity of the particle. Find the range on horizontal ground of the projectile thrown.(g=10m/s²)

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100m

200m

220m

120m

answer is C.

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Detailed Solution

The path of the particle will be a parabola, but along x-axis also motion of the particle will be accelerated. Time of flight of the projectile is

$T = \frac{2 u_{y}}{a_{y}} = \frac{2 u_{y}}{g} = \frac{2 \times 20 \sin 45^{0}}{10} = 2 \sqrt{2} s$

Horizontal range of the particle will be

$R = u_{x} T + \frac{1}{2} a_{x} T^{2}$

$a_{x} = \frac{q E}{m} = \frac{(2 \times 10^{- 6}) (2 \times 10^{7})}{1} = 40 m / s^{2}$

$R = (20 \cos 45^{0}) (2 \sqrt{2}) + \frac{1}{2} (40) {(2 \sqrt{2})}^{2}$

=40+160

=200m

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