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

Answer

A

Explanation

Terminal velocity is attained when magnetic force is equal to `mg sin theta`
:. `F_(m)=mg sin theta`
or `ilB=mg sin theta`
or `((e)/(R ))lB=mgsintheta`
or `((Bv_(T)l))/(R )=lB=mgsintheta`
:. `v_(T)=(mgRsintheta)/(B^(2)l^(2))`