A particle of mass m starts moving at `t =0` due to force `F =F_(0) sin omegat` where `F_(0)` and `omega` are constant Then correct statement is//are .

Options

A. it will stop first time at `(pi)/(omega)`
B. It will travel distance `S =(F_(0))/(momega^(2))` during this time .
C. During this distance maximum velocity of particle is `v_(max) =(F_(0))/(momega)` .
D. it will stop for first time at `2pi//omega`

Answer

C, D

Explanation

`F=F_(0)sin omegat = (mdv)/(dt)rArrunderset(0)overset(v)intdv=underset(0)overset(t)int(F_(0))/(m)sinomegatdt`
`V=(F_(0))/(mw)[1-cosomegat]`so at `t=pi//w`
`V=(2F_(0))/(momega):.(a)` is wrong. The max value of
`V =(F_(0))/(mw)` when `cos omegat = 0 :. (C)` is correct.
Now `(dS)/(dt) = (F_(0))/(momega)[1-cosmoegatt]`
`underset(0)overset(s)intdS=underset(0)overset(t)int(F_(0))/(momega)[1-cosomegat]`
`S=(F_(0))/(momega^(2))[omegat-sinomegat]att=pi//omega`
`S=(F_(0)pi)/(momega^(2)):.(B)` is wrong .