Verified Solution • 2025–26 Session
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QAIPM-2012-Ph-1759: NEET 2012 Physics - Class 12 AIPM-2012-Ph-1759 Solution: A compass needle which is allowed to move in a horizontal plane …
A compass needle which is allowed to move in a horizontal plane is taken to a geomagnetic pole. It will become rigid showing no movement will stay in any position will stay in north-south direction only will stay in east-west direction only
Multiple Choice Options
- A l 2 _ l 1 _ _ = 8 5 _
- B l 2 _ l 1 _ _ = 3 1 _
- C l 2 _ l 1 _ _ = 8 3 _
- D l 2 _ l 1 _ _ = 2 1 _
Step-by-Step Verified Solution
Let x is the resistance per unit length then
equivalent resistance R = R 1 R 2 R 1 + R 2
( x 1 l 1 ) ( x 2 l 2 ) x l 1 + x l 2
_ 8 3 = x l 1 l 1 l 2 + 1 ...(i)
also R 0 = x l 1 + x l 2
12 = x ( l 1 + l 2 )
12 = x l 2 ( l 1 l 2 + 1 ) ...(ii)
Now
( i ) ( i i ) _ 8 3 12 1 = x l 1 ( l 1 l 2 + 1 ) x l 2 ( l 1 l 2 + 1 )
= l 1 l 2 ( l 1 l 2 + 1 ) 2
( l 1 l 2 + 1 ) 2 _ 8 36 = l 1 l 2
( y 2 + 1 + 2 y ) _ 8 36 = y (where y = l 1 l 2 )
8y 2 + 8 + 16y = 36y
_ 8y 2 � 20y + 8 = 0
_ 2y 2 � 5y + 2 = 0
_ 2y 2 � 4y � y + 2 = 0
_ 2y (y � 2) � 1(y � 2) = 0
_ (2y � 1) (y � 2) = 0
_ y = l 1 l 2 = 1 2 or 2