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Q.

Two identical discs having radius R are rotating in opposite sense are joined with light rod having frictionless groove A and B and placed on rough horizontal surface as shown in figure. Initially translation velocity of each disc is zero. Then:
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a

Final velocity of B is  Rω06

b

Rod’s length will increase initially due to stress

c

Finally rod has tensile stress

d

Mechanical energy will decrease

answer is A, B, D.

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Detailed Solution

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 Angular momentum conservation gives
 (2ω0)mR22mR22(ω0)=2mvCR+2mR22ω' mR22ω0=2mvCR+mRvC      (Since  vC=ω'R) vC=Rω06
* Second figure shows that rod is under stress & hence its length will increase.
* Finally when the discs roll purely, there is no friction & hence to tensile stress 
* Since friction is kinetic therefore mechanical energy will decrease.

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