A pendulum consists of a bob of mass and a massless inextensible string of length . It is suspended from a fixed point at height above a frictionless horizontal floor. Initially, the bob of the pendulum is lying on the floor at rest vertically below the point of suspension. A horizontal impulse is imparted to the bob at some instant. After the bob slides for some distance, the string becomes taut and the bob lifts off the floor. The magnitude of the angular momentum of the pendulum about the point of suspension just before the bob lifts off is . The kinetic energy of the pendulum just after the lift-off is Joules.
The value of is ____.
The value of is ____.
Answer: 0.18
Solution
When the bob is on the floor and receives horizontal impulse , it moves horizontally with velocity:
The bob slides on the floor until the string becomes taut. At that moment, the perpendicular distance from the point of suspension to the velocity vector is m.
Angular momentum about the point of suspension:
So
The bob slides on the floor until the string becomes taut. At that moment, the perpendicular distance from the point of suspension to the velocity vector is m.
Angular momentum about the point of suspension:
So
JEE Advanced · 2021 · 03 Oct 2021 · Paper 2 · Numerical answer