Two identical uniform discs roll without slipping on two different surfaces A B and C D (see figure) starting at A and C with linear speeds υ 1 and υ 2 , respectively, and always remain in contact with the surfaces. If they reach B and D wi

Question

Two identical uniform discs roll without slipping on two different surfaces A B and C D (see figure) starting at A and C with linear speeds υ 1 and υ 2 , respectively, and always remain in contact with the surfaces. If they reach B and D with the same linear speed and υ 1 = 3 m/s, then υ 2 in m/s is g = 10 m s 2

Quantrex Academy · Accepted Answer

Correct answer: 7

K . E d = K . E T + K . E R o t = 1 2 m v 2 + 1 2 I c m w 2 = 1 2 m v 2 + 1 2 m r 2 2 v r 2 = 3 4 m v 2 K A + W g = K B = 3 4 m v 1 2 + m g × 30 = K B K C + W g = K D = 3 4 m v 2 2 + m g × 27 = K D K B = K D (Conversation of energy) ⇒ 3 4 m 3 2 - 3 4 m v 2 2 + 3 m g = 0 ⇒ v 2 2 = 49 ⇒ v = 7

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