A pendulum consists of a bob of mass $m =01\, kg$ and a massless inextensible string of length $L =10 \,m $ It is suspended from a fixed point at height $H =09 \,m$ 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 $P =02\, kg - m / s$ 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 $J \,kg - m ^{2} / s$ The kinetic energy of the pendulum just after the lift-off is $K$ Joules The value of $J$ is ______
A pendulum consists of a bob of mass $m =01\, kg$ and a massless inextensible string of length $L =10 \,m $ It is suspended from a fixed point at height $H =09 \,m$ 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 $P =02\, kg - m / s$ 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 $J \,kg - m ^{2} / s$ The kinetic energy of the pendulum just after the lift-off is $K$ Joules The value of $J$ is ______
Solution and Explanation
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Concepts Used:
System of Particles and Rotational Motion
- The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
- The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
- The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.