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A simple pendulum consisting of a mass \( M \) attached to a string of length \( L \) is released from rest at an angle \( \alpha \). A pin is located at a distance \( l \) below the pivot point. When the pendulum swings down, the string hits the pin as shown in the figure- \( \quad \). The maximum angle \( \theta \) which string makes with the vertical after hitting the pin is :
(A) \( \cos ^{-1}\left[\frac{L \cos \alpha+l}{L+l}\right] \)
(B) \( \cos ^{-1}\left[\frac{L \cos \alpha+l}{L-l}\right] \)
(C) \( \cos ^{-1}\left[\frac{L \cos \alpha-l}{L-l}\right] \)
(D) \( \cos ^{-1}\left[\frac{L \cos \alpha-l}{L+l}\right] \)
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