A particle of mass \( m \) is subjected to an attractive central force of magnitude \( k / r^{2}...

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A particle of mass \( m \) is subjected to an attractive central force of magnitude \( k / r^{2}, k \) being a constant. If at the instant when the particle is at an extreme position in its closed path, at a distance a from the centre of the force, its speed is \( \sqrt{k /(2 m a)} \), find the other extreme position.
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