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A rod of mass m and length L is kept on ...

A rod of mass m and length L is kept on a frictionless horizontal floor. A particle of same mass m moving perpendicular to the rod with a speed v strikes at the end of the rod. If coefficient of elasticity for the collision is 1 then calculate angular velocity acquired by the rod.

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To solve the problem, we need to analyze the collision between the particle and the rod, applying the principles of conservation of momentum and conservation of angular momentum. Here’s a step-by-step solution: ### Step 1: Understand the System We have a rod of mass \( m \) and length \( L \) resting on a frictionless surface. A particle of mass \( m \) is moving with speed \( v \) and strikes the end of the rod perpendicularly. ### Step 2: Conservation of Linear Momentum Since there are no external forces acting on the system, the linear momentum before and after the collision must be conserved. ...
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