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Question

A compass needle which is allowed to move in a horizontal plane is taken to a geomagnetic pole. It

(a) will stay in north-south direction only
(b) will stay in east-west direction only
(c) will become rigid showing no movement
(d) will stay in any position

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Solution

(d) will stay in any position

When taken to a geomagnetic pole, a compass needle that is allowed to move in a horizontal plane will try to suspend itself vertically to the horizontal plane containing the compass. In other words, the horizontal plane containing the compass will restrict the compass to suspend itself in vertical direction; hence, the compass will stay in any position.
However, a freely suspended magnet will become vertical at poles, with its north pole pointing towards Earth at its north pole (which is magnetic south).

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