A particle of specific charge `q/m = pi C kg^-1` is projected from the origin toward positive x-axis with a velocity of `10 ms^-1` in a uniform magnetic field `vec B = -2 hat k T.` The velocity `vec v` of particle after time `t=1/12 s` will be (in `ms^-1`)

Options

A. `5 [hat(i) + sqrt3 hat(j)]`
B. `5[sqrt3 hat(i) - hat(j)]`
C. `5 [3 hat(i) + hat(j)]`
D. `5 [hat(i) + hat(j)]`

Answer

C

Explanation

Time period, `T= (2pi m)/(qB)= (2pi )/(pi xx 2)= 1s`
Thus, particle will be at point P after `t= (1)/(12)`s
`:. vec(v) =10 [cos 30 hat(i) + sin 30 hat(j)]`
`rArr vec(v)= 10[(sqrt3)/(2) hat(i) + (1)/(2) hat(j)] =5 [sqrt3 hat(i) +hat(j)] ms^(-1)`