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A uniform rod AB which is free to swing in the vertical plane about a horizontal axis through A, is hanging freely. A particle of equal mass strikes the rod with a velocity v and gets stuck to it. Find the angular velocity of the combination immediately after the collision.

A uniform rod AB which is free to swing in the vertical plane about a horizontal axis through A, is hanging freely. A particle of equal mass strikes the rod with a velocity v and gets stuck to it. Find the angular velocity of the combination immediately after the collision.

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Grade:12th pass

1 Answers

Spandan Mallick
12 Points
5 years ago
First we have to find the net moment of inertia of the setup.
I = (mL^2/12)+(mL^2/2) = (7mL^2/12)
Now,
mvr = Iw 
=> m. v. (L/2) = (7mL^2/12) . w
=> w = 6v/7L.
 
Hope it helps. 
Spandan Mallick, JEE Aspirant.

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