Two small balls A and B, Each of Mass m, are joined rigidly to the ends of a light rigid rod length $l$ . The system lies on a smooth horizontal table. A particle of same mass moving with speed u perpendicularly to rod on the table strikes particle B, as shown, consider the following four situations and find the angular velocity $ω$ of rod after collision.
COLUMN - A COLUMN-B
i)
Rod AB lies freely, collision is elastic p) $ω = \frac{u}{l}$
ii)
Rod AB is hinged in the middle, collision is elastic q) $ω = \frac{u}{2 l}$
iii)
Rod AB lies freely, colliding particle sticks r) $ω = \frac{4 u}{3 l}$
iv)
Rod AB is hinged in the middle, colliding particle sticks s) $ω = \frac{2 u}{3 l}$

Question

Infinity Learn · Accepted Answer

i-q, ii-q, iii-p, iv-s

Detailed Solution

	COLUMN - A		COLUMN-B
i)	Rod AB lies freely, collision is elastic	p)	$ω = \frac{u}{l}$
ii)	Rod AB is hinged in the middle, collision is elastic	q)	$ω = \frac{u}{2 l}$
iii)	Rod AB lies freely, colliding particle sticks	r)	$ω = \frac{4 u}{3 l}$
iv)	Rod AB is hinged in the middle, colliding particle sticks	s)	$ω = \frac{2 u}{3 l}$