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In a magnetic field as shown, in Fig. tw...

In a magnetic field as shown, in Fig. two horizontal wires of same mass and length `l_(1) and l_(2)` are free to slide on different vertical rails with velocities `v_(1) and v_(2)` respectively. If the resistance of two circuits are same and `a_(1) and a_(2)` are acceleration of two horizontal wires respectively, the condition for `a_(1)gta_(2)` is

A

`(l_1)/(l_2) = (v_2)/(v_1)`

B

`(l_1)/(l_2) lt ((v_2)/(v_1))^(1//2)`

C

`(l_1)/(l_2) gt ((v_1)/(v_2))^(1//2)`

D

`(l_1)/(l_2) lt (v_1)/(v_2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`(B^(2)v_(1)l_(1)^(2))/(R)-mg=ma_(1)`...(i)
`(B^(2)v_(1)l_(2)^(2))/(R)-mg=ma_(1)-mg=ma_(2)` ...(ii)
`a_(1)-a_(2)=((B^2)/(mR))(v_(1)l_(1)^(2)-v_(2)l_(2)^(2))`
for `a_(1)gta_(2), v_(1)l_(1)^(2)gtv_(2)l_(2)^(2)`
`(l_1)/(l_2) gt ((v_2)/(v_1))^(1//2)`.
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