Question:
A smooth sphere A is moving on a frictionless horizontal plane with angular velocity $?$ and centre of mass velocity v. It collides elastically and head on with an identical sphere B at rest. Neglect friction everywhere. After the collision their angular speeds are $?_A$ and $?_B$ respectively. Then,
A smooth sphere A is moving on a frictionless horizontal plane with angular velocity $?$ and centre of mass velocity v. It collides elastically and head on with an identical sphere B at rest. Neglect friction everywhere. After the collision their angular speeds are $?_A$ and $?_B$ respectively. Then,
Updated On: Jun 14, 2022
- $?_A < ?_B$
- $?_A = ?_B$
- $?_A = ?$
- $?_B = ?$
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The Correct Option is C
Solution and Explanation
Since, it is head on elastic collision between two identical spheres, they will exchange their linear velocities i.e., A comes to rest and B starts moving with linear velocity v. As there is no friction anywhere, torque on both the spheres about their centre of mass is zero and their angular velocities remain unchanged. Therefore,
$?_A= ?$ and $?_B= 0.$
$?_A= ?$ and $?_B= 0.$
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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.