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A clay sphere is traveling horizontally with speed v when it strikes a rod of length L that is suspended from one end and has a rotational inertia of į ML’about its pivot point, as shown above. The clay sphere sticks to the rod, which begins to swing about the pivot. If both objects have mass M, the initial angular speed of the sphere-rod system just after the collision is
A. v/2L
B. 3v/4L
C. 3v/2L
D. 2v/L
E. 3v/L



Answer :

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Answer:

B. 3v/4L

Explanation:

The total angular momentum is conserved. The angular momentum of the sphere is equal to its linear momentum times the distance from the pivot point. The angular momentum of the sphere-rod system is equal to the combined moment of inertia times the angular velocity.

MvL = Iω

MvL = (ML² + ⅓ ML²) ω

MvL = ⁴/₃ ML² ω

v = ⁴/₃ L ω

ω = 3v / 4L

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