A conducting bar of 3m length is allowed to fall freely from 80m high tower, keeping it aligned along the East-West direction. Find the emf induced in the rod when it is 20m below the top of tower.
`g=10 ms^(-2) , B_h=0.7xx10^(-4)`T and angle of deep = `60^@` .

Options

A. 2.5 mV
B. 2.1 mV
C. 2.7 mV
D. 1.2 mV

Answer

B

Explanation

Here l=3 m
h=80 m
d=20 m
`g=10 ms^(-2)`
`B_h=0.7xx10^(-4)`T
`phi=60^@`
Put `v_0=0` in kinetic equation `v^2-v_0^2=2gd`
`therefore v^2=2gd`
`therefore v^2=2xx10xx20`
`therefore v^2=400`
`therefore` v=20 m/s
`rArr` Kinetic emf
E=Bvl
`=B_h cos phi vl`
`=0.7xx10^(-4) xx cos60^@xx20xx3`
`=0.7xx10^(-4)xx1/2xx20xx3`
`=2.1xx10^(-3)` V
`therefore` E=2.1 mV