There is a uniform electric field of strength `10^(3)V//m` along `y`-axis. A body of mass `1g` 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)

Options

A. 10
B. `5sqrt(2)`
C. `10sqrt(2)`
D. 20

Answer

C

Explanation

Given `v_(x) = 10 ms^(-1)`. Since the electric field is directed along the y-axis, the acceleration of the body along the y-direction is
`a_(y) = (qE)/(m) = (10^(-6) xx 10^(3))/(10^(-3)) = 1ms^(-2)`
Therefore, the velocity of the body along the y-axis at time t = 10 s is
`v_(y) = a_(y)t = 1 xx 10 = 10 ms^(-1)`
`:.` Resultant velocity
`v = sqrt(v_(x)^(2) + v_(y)^(2)) = sqrt((10)^(2) + (10)^(2)) = 10 sqrt(2) ms^(-1)`