A particle with mass m and positive charge q released from rest at the origin as shown in figure. There is a uniform electric field `E_(0) `in `+y` direction and uniform magnetic field `B_(0)` directed out of the page. The path of the particle as shown is called cycloid. The particle always moves in `x-y` plane. The velocity at any time t after the start is given as

The time for which the `y-` coordinate of the particle bomes maximum for the first time is

Options

A. `(m pi)/(qB_(0))`
B. `(2pim)/(qB_(0))`
C. `(pi m)/(qE_(0))`
D. `(2pi m)/(3q B_(0))`

Answer

A

Explanation

y will be maximum
`co ((qB_(0))/(m)t)=-1,(qB_(0))/(m)t=piimpliest=(pim)/(qB_(0))`