NTA Abhyas JEE Main2020PhysicsLaws of MotionPractice
A simple pendulum consisting of a mass M attached to a string of length L is released from rest at an angle α . 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. If the particle doesn't undergo a complete vertical circle, then the maximum angle θ < π 2 through which the string swings after hitting the pin is
Options
- Acos - 1 L cos α + l L + l
- Bcos - 1 L cos α - l L - l
- Ccos - 1 ⁡ L cos ⁡ α + l   L - l
- Dcos - 1 ⁡ L cos ⁡ α - l   L + l
Correct answer
B. cos - 1 L cos α - l L - l
Step-by-step solution
At the bottom most point, square of speed of bob, v 2 = 2 g L 1 – c o s α It will rise further to a height, h = v 2 2 g = L 1 - cos α or L - l 1 - cos θ = L 1 - cos α ∴ θ = cos - 1 L cos α - l L - l