A copper rod of mass `m` slides under gravity on two smooth parallel rails `l` distance apart set at an angle `theta` to the horizontal. At the bottom, the rails are joined by a resistance `R`.

There is a uniform magnetic field perpendicular to the plane of the rails. the terminal valocity of the rod is

Options

A. `(mgR cos theta)/(B^(2)l^(2))`
B. `(mg R sin theta)/(B^(2) l^(2))`
C. `(mgR tan theta)/(B^(2) l^(2))`
D. `(mgR cot theta)/(B^(2)l^(2))`

Answer

B

Explanation

Terminal velocity is attained when magnetic force is equal to `mg sin theta`
`therefore F_(m) = mg sin theta`

or `= mg sin theta`
or `(e/R) lB = mg sin theta`
or `(Bv_(T)l)/R xx lB = mg sin theta`
`therefore v_(T) = (mgR sin theta)/(B^(2)l^(2))`