question_answer

There is a uniform electric field of strength \[{{10}^{3}}\,V/m\] along y-axis. A body of mass 1g and charge \[\text{1}{{0}^{\text{6}}}C\] is projected into the field from origin along the positive x-axis with a velocity 10m/s. Its speed in m/s after 10s is (Neglect gravitation) [EAMCET 2001]

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 v = u + at Þ \[{{v}_{y}}=0+\frac{QE}{m}.\,t=\frac{{{10}^{-6}}\times {{10}^{3}}}{{{10}^{-3}}}\times 10=10\,m/\text{sec}\] For horizontal motion ? It?s horizontal velocity remains the same i.e. after 10 sec, horizontal velocity of body vx = 10 m/sec. Velocity after 10 sec \[v=\sqrt{v_{x}^{2}+v_{y}^{2}}\]\[=10\sqrt{2}\,m/sec\]