$A$ monkey is descending from the branch of a tree with constant acceleration. If the breaking strength of the branch is $75 \%$ of the weight of the monkey,what is the minimum acceleration with which the monkey can slide down without breaking the branch?

$A$ small ball $B$ of mass $m$ is suspended with a light inelastic string of length $L$ from a block $A$ of the same mass $m$,which can move on a smooth horizontal surface as shown in the figure. The ball is displaced by an angle $\theta$ from the equilibrium position and then released. The maximum velocity of the block during the subsequent motion of the system after the release of the ball is

If a ship of mass $4 \times 10^{7} \,kg$ initially at rest is pulled by a force of $5 \times 10^{4} \,N$ through a distance of $4 \,m$, then the speed of the ship will be (resistance due to water is negligible). (in $\,ms^{-1}$)

Two blocks of masses $5\, kg$ and $4\, kg$ are in contact with each other on a frictionless table. When a horizontal force of $9\, N$ is applied to the block of mass $5\, kg$,then the value of the force of contact between the two blocks is ........ $N$.

$A$ balloon of mass $M$ descends with an acceleration $a (< g)$. What mass needs to be removed from the balloon so that it starts ascending with acceleration $a$?

The arrangement of a two-block system is as shown. Assuming the surfaces to be frictionless,the net force acting on the $1 \, kg$ and $2 \, kg$ blocks are,respectively: