In the figure shown,the velocities of differe | vedclass

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(A) Let the velocity of the left pulley $P_1$ be $v_{P_1}$ and the right pulley $P_2$ be $v_{P_2}$.Taking downward direction as positive:For pulley $P

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$4$

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(A) Let the velocity of the left pulley $P_1$ be $v_{P_1}$ and the right pulley $P_2$ be $v_{P_2}$.Taking downward direction as positive:For pulley $P_1$,the blocks $A$ and $B$ move with velocities $v_A = 6\,m/s$ (downward) and $v_B = -6\,m/s$ (upward).The velocity of pulley $P_1$ is $v_{P_1} = \frac{v_A + v_B}{2} = \frac{6 + (-6)}{2} = 0\,m/s$.Since the pulleys $P_1$ and $P_2$ are connected by a string over a fixed pulley,their velocities must be equal in magnitude but opposite in direction (if one moves up,the other moves down).Thus,$v_{P_2} = -v_{P_1} = 0\,m/s$.For pulley $P_2$,the blocks $C$ and $D$ move with velocities $v_C$ and $v_D = 4\,m/s$ (downward).The velocity of pulley $P_2$ is $v_{P_2} = \frac{v_C + v_D}{2}$.Substituting the values: $0 = \frac{v_C + 4}{2}$.$v_C + 4 = 0 \implies v_C = -4\,m/s$.The magnitude of the velocity of $C$ is $4\,m/s$.

In the figure shown,the velocities of different blocks are given. The velocity of $C$ is $.........\,m/s$.

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