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 ......... $m / s ^2$ $\left(g=10 \,m / s ^2\right)$

Two equal masses $A$ and $B$ are arranged as shown in the figure. Pulley and string are ideal and there is no friction. Block $A$ has a speed $u$ in the downward direction. The speed of the block $B$ is :-

In the arrangement shown in figure the ends $P$ and $Q$ of an unstretchable string move downwards with uniform speed $ U$. Pulleys $A$ and $B$ are fixed. Mass $M$ moves upwards with a speed

If block $A$ is moving with an acceleration of $5\,m/s^2$, the acceleration of $B$ w.r.t. ground is