Kinematics Question 559
Question: A simple pendulum oscillates in a vertical plane.When it passes through the mean position, the tension in the string is 3 times the weight of the pendulum bob.What is the maximum displacement of the pendulum of the string with respect to the vertical [Or it’ssa JEE 2002]
Options:
A) $ 30^{o} $
B) $ 45^{o} $
C) $ 60^{o} $
D) $ 90^{o} $
Show Answer
Answer:
Correct Answer: D
Solution:
Tension at mean position, $ mg+\frac{mv^{2}}{r}=3mg $
$ v=\sqrt{2gl} $ -(i) and if the body d it’splaces by angle q with the vertical then
$ v=\sqrt{2gl(1-\cos \theta )} $ -(ii) Comparing (i) and (ii), $ \cos \theta =0 $
therefore $ \theta =90{}^\circ $
