A simple pendulum consisting of a mass M attached to a string of … - Vidyadip

MCQ

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. 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
${\cos ^{ - 1}}\left[ {\frac{{L\cos \alpha + l}}{{L - l}}} \right]$
✓
${\cos ^{ - 1}}\left[ {\frac{{L\cos \alpha - l}}{{L - l}}} \right]$
D
${\cos ^{ - 1}}\left[ {\frac{{L\cos \alpha - l}}{{L + l}}} \right]$

✓

Answer

Correct option: C.

${\cos ^{ - 1}}\left[ {\frac{{L\cos \alpha - l}}{{L - l}}} \right]$

c
$0 + mg (L \,cos\, \alpha -l) = mg(L -l)cos \alpha$

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