In the given figure, two elastic rods \( P \) and \( Q \) are rigidly joined to end supports. A ...

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In the given figure, two elastic rods \( P \) and \( Q \) are rigidly joined to end supports. A small mass \( m \) is moving with velocity \( v \) between the rods. All collisions are assumed to be elastic and the surface is given to be smooth. The time period of small mass \( m \) will be ( \( A= \) area of cross-section, \( Y= \) Youngs modulus, \( L= \) length of each rod)
P
(a) \( \frac{2 L}{v}+2 \pi \sqrt{\frac{m L}{A Y}} \)
(b) \( \frac{2 L}{v}+2 \pi \sqrt{\frac{2 m L}{A Y}} \)
(c) \( \frac{2 L}{v}+\pi \sqrt{\frac{m L}{A Y}} \)
(d) \( \frac{2 L}{v} \)
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