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. (a) `(1)/(2)[(IBl)/(m) - 2g]t^(2)`
B. (b) `(1)/(2)[(Ibl)/(m) xx (1)/(costheta) - 2g sin theta]t^(2)`
C. (c ) `(1)/(2)[(Ibl)/(m) - 2g sin theta]t^(2)`
D. (d) `(1)/(2)[(Ibl)/(m)(cos 2theta)/(cos theta) - 2ssin theta]t^(2)`

Answer

D

Explanation

(d) The front view of the arrangement is shown in Fig. S3. 61

From initial condition, `mg sin theta = mumg cos theta`
`rarr` `mu = tantheta`
`ma = Ibl cos theta - mg sin theta - mu N`
`N = mg cos theta + IBl sin theta`
`rarr` `a = (IBl)/(m)cos theta - 2g sin theta - (IBl)/(m)(sin^(2) theta)/(cos theta)`
`= (IBl)/(m)(cos 2theta)/(cos theta) - 2g sin theta`
Now, `s = (1)/(2)at^(2) = (1)/(2)[(IBl)/(m)(cos2theta)/(cos theta) - 2g sin theta]t^(2)`