Rotational MotionHard
Question
A rod of mass ′m′ is suspended vertically from a hinge A and is free to rotate along a horizontal axis passing through A as shown. A ball of mass m moving horizontally with speed u hits the bottom of the vertical rod elastically at t = 0 sec. Then the linear momentum of the ball and rod system after the collision
Options
A.is same as before the collision
B.becomes lesser than before collision
C.becomes more than before the collision
D.no inference can be drawn
Solution
After collision end of the rod which is at hinge A try to move left so hinge provide force to the rod towards right.
Proof:
Conservation of angular momentum: let U′ is final velocity of block.
mul = m u′l + Iω
Conservation of energy
1/2 mu2 = 1/2 mu′2 + 1/2 Iω2
solving these equation:
We get Lω = 3/2 V
Vcom = 3/4V
V′ = V/2
∴ net linear momentum of the system will be :
3/4MV + MV/2 = 5MV/4
Thus linear momentum will increase
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