$A$ uniform chain of length $2L$ is hanging in equilibrium over a small,smooth pulley. If end $B$ is given a slightly downward displacement $x$,the imbalance causes an acceleration. The acceleration of the chain when it has been displaced by distance $x$ is:

Two blocks $A$ and $B$ of masses $1.5 \ kg$ and $0.5 \ kg$ respectively are connected by a massless inextensible string passing over a frictionless pulley as shown in the figure. Block $A$ is lifted until block $B$ touches the ground and then block $A$ is released. The initial height of block $A$ is $80 \ cm$ when block $B$ just touches the ground. The maximum height reached by block $B$ from the ground after the block $A$ falls on the ground is (in $cm$)

In the figure shown,both blocks are released from rest. Find the time taken for them to cross each other. (Assume $g = 10 \ m/s^2$)

Three blocks $A, B$ and $C$ are suspended as shown in the figure. The mass of each block $A$ and $C$ is $m$. If the system is in equilibrium and the mass of $B$ is $M$,then:

Three blocks $M_1, M_2, M_3$ having masses $4 \ kg, 6 \ kg$ and $10 \ kg$ respectively are hanging from a smooth pulley using ropes $1, 2$ and $3$ as shown in the figure. The tension in the rope $1, T_1$,when they are moving upward with an acceleration of $2 \ m/s^2$ is ............... $N$ (if $g = 10 \ m/s^2$).

$A$ light string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$ (where $m_2 > m_1$). If the acceleration of the system is $\frac{g}{\sqrt{2}}$,then the ratio of the masses $\frac{m_1}{m_2}$ is: