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Question:

Two identical uniform discs roll without slipping on two different surfaces AB and CD starting at A and C with linear speed ʋ₁ and ʋ₂, respectively, and always remain in contact with the surfaces. If they reach B and D with the same linear speed and ʋ₁=3m/s, then ʋ₂ in m/s is (g=10m/s²)

Solution:

Ktotal=Ktr+Krot=1/2mv²+1/2Iω²=1/2mv²+1/2(mR²/2)(v/R)²=3/4mv²
Since velocity of both the discs are same at B , using conservation of energy,
3/4mv₁²+mg(30)=3/4mv₂²+mg(27)
Putting v₁=3 and solving
v₂²=49
⇒v₂=7