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Q.

Two girls Sita and Gita are skating towards each other on smooth ice along parallel lines as shown in figure. The distance between the lines is l. The mass of two girls are m1 and m2 m1 <m2 and their respective velocity are v1 and v2 v2>v1 . One of the girls holds a stick of length l and negligible mass. When the girls pass each other, second girl grasps the stick and the girls move together, each of them on either side of the stick. Mark the correct statements

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a

In the center of mass reference frame of system both the girls have momentum of equal magnitude.

b

If the girls start moving towards each other by pulling the stick, angular velocity of system will increase.

c

After the girl has grabbed the rod, system rotates in anti-clock wise sense while center of mass translates towards left.

d

Angular momentum of system about center of mass increases.

answer is A, C, D.

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Detailed Solution

P1 c=P2  c=μ Vrel

Angular momentum of system would remain conserved as there is no extremal torque.

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    vcm= m1v1-m2v2m1+m2               m2v2 >m1v1

 Therefore vcm towards left. and would not change. Total initial L of system just before striking was in anti-clockwise sense, so after striking also it would remain in the same sense.

 

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