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[hati+sqrt3hatj]`
B. `5[sqrt3hati+hatj]`
C. `5[sqrt3hati-hatj]`
D. `5[hati+hatj]`

Answer

B

Explanation

Time period, `T=(2pim)/(qB)=(2pi)/(pixx2)=1s`

Thus, particle will be at point P after `t=1/12s`
`vecv=10[cos30hati+sin30hatj]`
`vecv=10[sqrt3/2hati+1/2hatj]=5[sqrt3hati+hatj]ms^-1`