Work Energy And Power Question 140
Question: A simple pendulum consisting of a mass $ M $ attached to a string of length L is released from rest at an angle $ a $ . 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 the string makes with the vertical after hitting the pin is
Options:
A) $ {{\cos }^{1}}[ \frac{L\cos a+l}{L+l} ] $
B) $ {{\cos }^{1}}[ \frac{L\cos a+l}{L-l} ] $
C) $ {{\cos }^{1}}[ \frac{L\cos a-l}{L-l} ] $
D) $ {{\cos }^{1}}[ \frac{L\cos a-l}{L+l} ] $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Since the pendulum started with no kinetic energy.
Conservation of energy, implies that the potential energy at $ {Q _{\max }} $ must be equal to the original potential energy, i.e., the vertical position will be same.
Therefore, $ L\cos \alpha =l+(L-1)cos\theta $
$ \Rightarrow \cos \theta =\frac{L\cos \alpha -l}{L-1} $
$ \Rightarrow \theta ={{\cos }^{-1}}[ \frac{L\cos \alpha -l}{L-l} ] $
