A ball suspended by a thread swings in a vertical plane, so that its acceleration in the extreme...

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A ball suspended by a thread swings in a vertical plane, so that its acceleration in the extreme position and lowest position are equal. The angle \( \theta \) of thread deflection in the extreme position will be
(a) \( \tan ^{-1}(2) \)
(b) \( \tan ^{-1}(\sqrt{2}) \)
(c) \( \tan ^{-1}\left(\frac{1}{2}\right) \)
(d) \( 2 \tan ^{-1}\left(\frac{1}{2}\right) \)
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