A train of mass 100 tons `(1` tons `=1000kg)` runs on a meter gauge track ( distance between the two rails is `1m)`. The coefficient of friction between the rails and the train is `0045`. The train is powered by an electric engine of `90%` efficiency. The train is moving with uniform speed of `72 kmph` at its highest speed limilt . Horizontal and vertical component of earth's magnetic field and `B_(H)=10^(-5)T` and `B_(V)=2xx10^(-5)T`. Assume the body of the train and rails to be perfectly conducting.
If now a resistor of `10^(-3)Omega` is attached of between the rwo rails, the extra units of energy ( electricity) consumed dueing a `324 km` rund of the train is ( 1 unit of power `=1kW` Hour ) ( assume the speed of train to remain unchanged.

Options

A. `8xx10^(-4)KW `hour
B. `8xx10^(-5)` KW hour
C. `8xx10^(-6) KW` hour
D. `8xx10^(-7)KW` hour

Answer

D

Explanation

`(D)` Time taken `=(324)/(72)=(9)/(2)` hour
extra power engine `=` power dissipated in resistor
`=(epsilon^(2))/(R)=((40xx10^(-5))^(2))/(10^(-3))=16xx10^(-5)`watt
engine will be `(16xx10^(-5))/(10^(-3))`watt
Energy consumed `=(16xx10^(-5))/(0.9)`watt `xx(9)/(2)`hour
`=8xx10^(-7)KW` hour