question_answer

There is a uniform electric field of strength \[{{10}^{3}}\,V/m\] along y-axis. A body of mass 1 g and charge \[{{10}^{6}}\,C\] is projected into the field from origin along the positive x-axis with a velocity 10 m/s. Its speed in m/s after 10 s is (neglect gravitation)

A) 10                                

B) \[5\sqrt{2}\,\]

C) \[10\sqrt{2}\,\]              

D) 20

Correct Answer: C

Solution :

Body moves along the parabolic path. For vertical motion : By using \[\operatorname{v} =u + at\] \[\Rightarrow \,\,\,{{\nu }_{y}}=0+\frac{QE}{m}\,\,\cdot \,\,t=\,\,\frac{{{10}^{-6}}\times {{10}^{3}}}{{{10}^{-3}}}\,\,\times 10=10\,m/s\] For horizontal motion-Its horizontal velocity remains the same, i.e., after 10 s, horizontal velocity of body \[{{v}_{x}}\,\,=\,\,10\,m/s.\] Velocity after 10 s \[\nu =\sqrt{\nu _{x}^{2}+\nu _{y}^{2}}\,\,=\,\,10\sqrt{2}\,m/s\]