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Question

# Consider a uniform rod of mass M=4m and length L pivoted about its centre. A mass m moving with a velocity V making an angle θ=π4 to the rod's long axis collides with one end of the rod, and sticks to it. The angular speed of the rod-mass system just after the collision is:

A
372VL
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B
37VL
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C
327VL
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D
47VL
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Solution

## The correct option is C 3√27VL Angular momentum of the rod-mass system about point O is ⇒L=(mg×0)+mV√2×L2=mVL2√2 Let, I be the moment of inertia about O of the rod-mass system, and, ω be the angular speed just after collision. I=4mL212+mL24=712mL2 L=Iω ⇒mVL2√2=712mL2×ω ∴ω=6V7√2L=3√2V7L Hence, option (C) is correct.

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