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 $(g = 10 \frac{m}{s^{2}})$

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Aicharya · Accepted Answer

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

Two identical uniform discs roll without slipping on two different surfaces A B and C D (see figure)…

Solution