Three masses $m_1 = 4 \text{ kg}$, $m_2 = 4 \text{ kg}$, and $m_3 = 6 \text{ kg}$ are suspended from a fixed smooth frictionless pulley as shown in the figure. The value of $T_1/T_2$ is . . . . . . . (Take $g = 10 \text{ m/s}^2$)

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 $cm$)

The maximum acceleration with which a body of mass $200 \, kg$ is lowered into a well using a rope having a breaking force of $50 \, kg$-wt is (Acceleration due to gravity $= 10 \, ms^{-2}$) (in $ \, ms^{-2}$)

One end of a massless rope,which passes over a massless and frictionless pulley $P$,is tied to a hook while the other is free. The maximum tension the rope can bear is $360 \ N$. With what value of maximum safe acceleration (in $m \ s^{-2}$) can a man of $60 \ kg$ climb on the rope?

Three masses of $1\, kg$,$6\, kg$,and $3\, kg$ are connected to each other with threads and are placed on a table as shown in the figure. The acceleration with which the system is moving is $....... \, ms^{-2}$. (Take $g = 10\, ms^{-2}$)

$A$ 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: