A particle of charge per unit mass `alpha` is released from origin with a velocity `vecv=v_(0)hati` in a magnetic field
`vec(B)=-B_(0)hatk` for `xle(sqrt(3))/2 (v_(0))/(B_(0)alpha)`
and `vec(B)=0` for `xgt(sqrt(3))/2 (v_(0))/(B_(0)alpha)`
The `x`-coordinate of the particle at time `t((pi)/(3B_(0)alpha))` would be

Options

A. `(sqrt(3))/(2)(upsilon_(0))/(B_(0)alpha)+(sqrt(3))/(2)upsilon_(0)(t-(pi)/(B_(0)alpha))`
B. `(sqrt(3))/(2)(upsilon_(0))/(B_(0)alpha)+upsilon_(0)(t-(pi)/(3B_(0)alpha))`
C. `(sqrt(3))/(2)(upsilon_(0))/(B_(0)alpha)+(upsilon_(0))/(2)(t-(pi)/(3B_(0)alpha))`
D. `(sqrt(3))/(2)(upsilon_(0))/(B_(0)alpha)+(upsilon_(0)t)/(2)`

Answer

C

Explanation

`r=(m upsilon_(0))/(B_(0)q)=(upsilon_(0))/(B_(0)alpha)`
`(x)/(r)=(sqrt(3))/(2)=sintheta`
`:. theta=60^(@)" "t_(OA)=(T)/(6)=(pi)/(3B_(0)alpha)`