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Asked by keshavgoyal9pro | 06 Dec, 2022, 14:25: PM

Expert Answer

The mass 1 kg at end A of the rod is increased to 2 kg due to the additional 1 kg mass that got sticked to mass at A.

Hence the speed of mass at end A has decreased while the speed of mass at B is not affected .

This difference in speed gives rotational motion about the end point B of rod .

Speed of rotation ω of the system after collision is determined by conservation of angular momentum

(m v r ) = I ω

where LHS is angular momentum just before collision and RHS is angular momentum just after collision .

m is mass at the point A before collision , v is speed of mass at A , r is distance of mass from point B and

I is moment of inertia of system of masses attached to rod when the rod is rotating .

Moment of inertia I about the axis passing through point A = (2m) r²

begin mathsize 14px style omega space equals space fraction numerator m space v space r over denominator left parenthesis 2 m right parenthesis space r to the power of 2 to the power of space end exponent end fraction space equals space fraction numerator v over denominator 2 r end fraction space equals space 4 over 2 space equals space 2 space r a d divided by s end style

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linear speed of mass at a = ω r = 2 × 1 m/s = 2 m/s

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mass at B is unaffected , hence it will move with speed 4 m/s

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speed of centre of mass

begin mathsize 14px style v subscript c m end subscript space equals space fraction numerator left parenthesis 2 m right parenthesis cross times 2 space plus space m space cross times 4 over denominator 3 m end fraction space equals space 8 over 3 space m divided by s end style

Answered by Thiyagarajan K | 09 Dec, 2022, 17:14: PM

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