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

An elevator accelerates upwards at a constant rate. A uniform string of length $L$ and mass $m$ supports a small block of mass $M$ that hangs from the ceiling of the elevator. The tension at distance $l$ from the ceiling is $T$ . The acceleration of the elevator is

Three blocks of masses $m_1=4 \,kg , m_2=2 \,kg , m_3=4 \,kg$ are connected with ideal strings passing over a smooth. massless pulley as shown in figure. The acceleration of blocks will be ......... $m / s ^2$ $\left(g=10 \,m / s ^2\right)$

Find the velocity of the hanging block if the velocities of the free ends of the rope are as indicated in the figure.

If pulleys shown in the diagram are smooth and massless and $a_1$ and $a_2$ are acceleration of blocks of mass $4 \,kg$ and $8 \,kg$ respectively, then

If acceleration of $A$ is $2 \,\,m/s^2$ to left and acceleration of $B$ is $1\,\,m/s^2$ to left, then acceleration of $C$ is