A conducting wire of length `l` and mass `m` is placed on two inclined rails as shown in figure. A current `I` is flowig in the wire in the direction shown When no magnetic field is present in the region, the wire is just on the verge of sliding. When a vertically upward magnetic field is switched on, the wire starts moving up the incline. The distance travelled by the wire as a function of time `t` will be

Options

A. `1/2[(IBl)/(m)-2g]t^(2)`
B. `1/2[(IBl)/(m) xx 1/(cos theta)-2g sin theta]t^(2)`
C. `1/2[(IBl)/(m) -2gsin theta]t^(2)`
D. `1/2[(IBl)/(m) (cos 2theta)/(cos theta) -2gsin theta]t^(2)`

Answer

D

Explanation

The front view of the arrangement is shown in the figure.
For initial condition,
`mg sintheta = mug costheta`
`rArr mu = tan theta`
`ma = Ibl costheta - mg sintheta - mu N`
`N=mg costheta + I"B"lsin theta`
`rArr a =(Ibl)/m costheta - 2g costheta - (IBl)/m (sin^(2)theta)/(cos theta)`
`=(IBl)/(m)(cos 2theta)/(cos theta) -2g sinthea`
Now, `s=1/2 at^(2) = 1/2[(IBl)/m (cos 2theta)/(cos theta) - 2g sin theta]t^(2)`