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 :-

A balloon of mass $m$ is descending down with an acceleration $\frac{g}{2}$.  How much mass should be removed from it so that it starts moving up with same acceleration?

The boxes of masses $2\, {kg}$ and $8\, {kg}$ are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass $8\; {kg}$ to strike the ground starting from rest. (use $\left.{g}=10\, {m} / {s}^{2}\right)$ (in ${s}$)

A rod of length $L$ leans against a smooth vertical wall while its other end is on a smooth floor. The end that leans against the wall moves uniformly vertically downward. Select the correct alternative

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

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