Question

The maximum angular displacement of simple pendulum of length $ l $ is $ \theta . $ Its maximum kinetic energy will be

• A. $ mgl\text{ }sin\theta $
• B. $ mgl\text{ }(1+sin\theta ) $ )
• C. $ mgl(1+cos\theta ) $
• D. $ mgl\text{ }(1-\cos \theta ) $

Answer 1

Answer: (D)

$ h=l-l\cos \theta $
The energy of pendulum at point A will be completely potential energy at point B will be kinetic energy.
$ \Rightarrow $ $ \frac{1}{2}m{{v}^{2}}=mgh $
$ \frac{1}{2}m{{v}^{2}}=mgl(1-\cos \theta ) $